Classical Economics
Classical macroeconomics emerged as a reaction against mercantilism, a set of doctrines associated with the rise of the nation state in Europe during the sixteenth and seventeenth centuries. Mercantilist thought emphasized bullionism, the belief that a nation’s wealth depended on its stock of precious metals, and argued for extensive state intervention to guide economic development. Governments attempted to secure trade surpluses through export subsidies, import duties, and colonial expansion.
In contrast, classical economists emphasized the role of real factors in determining the “wealth of nations.” They stressed the optimizing behaviour of individuals and firms and the efficiency of the free-market mechanism when left free from government interference. Classical analysis was primarily a real analysis: economic growth resulted from increases in factor inputs and improvements in production techniques. Money was viewed as playing only a limited role, serving mainly as a medium of exchange. Most economic questions could be answered without explicit reference to monetary variables.
Because of its emphasis on real factors and market efficiency, classical macroeconomics is best interpreted as a long-run analysis.
Classical economists believed that the free-market mechanism would always provide markets for any goods produced. In aggregate terms, production of output was assumed to generate sufficient demand to purchase that output. Consequently, classical economists devoted little attention to the determination of aggregate demand.
Two central features of classical macroeconomics followed from this perspective:
- Output and employment are determined by real factors, not by money.
- The economy has strong self-adjusting tendencies, making government intervention unnecessary and potentially harmful.
Although classical economists acknowledged that the economy could deviate temporarily from equilibrium, they believed such deviations would be short-lived. Market forces would operate quickly to restore full employment equilibrium. Persistent mass unemployment, as experienced during the 1930s, therefore posed a serious challenge to classical theory.
Output and Employment Determination
Output (Production): What determines real output?
A key component of the classical model is the short-run production function1. At the micro level, a production function expresses the maximum amount of output that a firm can produce from any given amounts of factor inputs. The more inputs of labour (L) and capital (K) that a firm uses, the greater will be the output produced (providing the inputs are used effectively).
However, in the short run, it is assumed that the only variable input is labour. The amount of capital input and the state of technology are taken as constant. When we consider the economy as a whole the quantity of aggregate output (GDP=Y) will also depend on the amount of inputs used and how efficiently they are used.
This relationship, known as the short-run aggregate production function, can be written in the following form:
Y=AF(K,L)
Output Determination
In the short-run aggregate production function (Y=AF(K,L)):
- Y= real output per period,
- K= the quantity of capital inputs (plant and equipment) used per period,
- L= the quantity of labour inputs used per period,
- A= an index of total factor productivity, and
- F= a function which relates real output to the inputs of K and L.
The symbol A represents the impact of improvements in technology and any other influences which raise the overall effectiveness of an economy’s use of its factors of production.
The short-run aggregate production function simply tells us that aggregate output will depend on the amount of labour employed, given the existing capital stock, technology and organization of inputs. For the short run, the stock of capital is assumed to be fixed. The state of technology and the population are also assumed to be constant over the period considered. For this short-run period, output varies solely with variations in the labour input (L) drawn from the fixed population.
The following table demonstrates the relationship between Labour (L) and Output (Y), illustrating the concept of Marginal Product of Labour (MPL = ΔY / ΔL):
The production function has several characteristics. At low levels of labour input, the function is a straight line. The slope of the line gives the increase in output for a given increment in labour input, so this straight-line (constant-slope) portion of the production function exhibits constant returns to scale. For very low levels of labour utilization, it might be presumed that additional workers could be applied to a given amount of plant and equipment without a fall in the productivity of the last worker hired.
For the most part, we consider situations where adding additional labour will result in increased total output, but where the size of the increases to output declines as more labour is employed. This portion of the production function exhibits diminishing returns to scale. Negative returns to scale occur when additional labour input results in decreased total output.
Marginal Product of Labor (MPL) is the addition to total output due to the addition of a unit of labour (the quantity of other inputs being held constant). The MPL is the slope of the production function (ΔY / ΔL).
- In the range of constant returns to scale, as L increases, the slope of the line is flat.
- However, as more workers are hired, the slope becomes negative, indicating that although the marginal product of each worker hired is positive, it is less than the marginal product of the previous worker. This area represents diminishing returns to scale.
- The marginal product of the additional worker is below the horizontal axis in the area of negative returns to scale.
The short-run production function is a technological relationship that determines the level of output given the level of labour input (employment). The capital stock, along with the existing level of technology and skill level of the workforce, is being held constant.
The short-run aggregate production function displays certain properties. Three points are worth noting:
- Positive Relationship: For given values of A and K there is a positive relationship between employment (L) and output (Y), shown as a movement along the production function from, for example, point a to b.
- Diminishing Returns: The production function exhibits diminishing returns to the variable input, labour. This is indicated by the slope of the production function (ΔY/ΔL) which declines as employment increases. Successive increases in the amount of labour employed yield less and less additional output. Since ΔY/ΔL measures the marginal product of labour (MPL), we can see by the slope of the production function that an increase in employment is associated with a declining marginal product of labour. This is illustrated where MPL is both positive and diminishing (MPL declines as employment expands from L₀ to L₁; that is, MPLₐ > MPLb).
- Shifts in the Function: The production function will shift upwards if the capital input is increased and/or there is an increase in the productivity of the inputs represented by an increase in the value of A (for example, a technological improvement). Such a change is shown by a shift in the production function from Y to Y* caused by A increasing to A*. The impact of the upward shift of the production function causes the MPL schedule to shift up from MPL to MPL*. Following such a change the productivity of labour increases (L₀ amount of labour employed can now produce Y₁ rather than Y₀ amount of output).
Employment Determination
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Employment Determination
Classical economists assumed that the quantity of labour employed would be determined by the forces of demand and supply in the labour market. To see how the aggregate level of employment is determined in the classical model, we must examine the classical economists’ model of the labour market.
According to the assumptions:
- Labour market works well.
- Firms and individual workers optimize. They have perfect information about relevant prices.
- There are no barriers to the adjustment of money wages (wages are perfectly flexible); the market clears.
The purchasers of labour services are firms. To see how the aggregate demand for labour is determined, we begin by considering the demand for labour on the part of an individual firm, denoted the ith firm.
In the classical model, firms are perfect competitors that choose their output to maximize profits. The perfectly competitive firm will increase output until the marginal cost of producing a unit of output is equal to the marginal revenue received from its sale:
MCᵢ = MRᵢ
For the perfectly competitive firm, marginal revenue is equal to product price (P): MRᵢ = P.
And then we can write the profit-maximizing rule as: MCᵢ = P
Employment Determination — Labour Demand
Because labour is the only variable factor of production, the marginal cost of each additional unit of output is the marginal labour cost. Marginal labour cost equals the money wage divided by the number of units of output produced by the additional unit of labour, which is marginal product of labour (MPL).
Thus, marginal cost for the ith firm (MCᵢ) is equal to the money wage (W) divided by the marginal product of labour for that firm (MPLᵢ):
MCᵢ = W / MPLᵢ
Since the condition for short-run profit maximization in the perfectly competitive market is MCᵢ = P, substituting the expression for marginal cost into the equation shows the short-run profit-maximizing position for the firm buying labour in the market for inputs:
P = W / MPLᵢ = MCᵢ
Multiplying both sides of this equation by MPL and dividing both sides by P gives the expression:
MPLᵢ = W / P
The profit maximization condition in the equation above can be explained as follows: The firm will hire up to the point where the additional output obtained by hiring one more worker (MPL) is just equal to the real wage (W/P) paid to hire that worker.
We can find the same result by a different reasoning:
If a firm hires labour within a competitive labour market, a money wage equal to W must be paid to each extra worker. The additional cost of hiring an extra unit of labour will be WΔLᵢ.
The extra revenue generated by an additional worker is the extra output produced (ΔQᵢ) multiplied by the price of the firm’s product (P). The additional revenue is therefore PΔQᵢ.
A profit-maximizing firm will hire labour as long as WΔLᵢ < PΔQᵢ. To maximize profits requires satisfaction of the following condition:
PΔQᵢ = WΔLᵢ
This is equivalent to:
ΔQᵢ / ΔLᵢ = W / P
Since ΔQᵢ / ΔLᵢ is the marginal product of labour, a firm should hire labour until the marginal product of labour equals the real wage rate:
MPLᵢ = W / P
Because the MPL is a declining function of the amount of labour employed, owing to the influence of diminishing returns, the MPL curve is downward-sloping.
Since we have shown that profits will be maximized when a firm equates the MPL with W/P, the marginal product of labour curve is equivalent to the firm’s demand curve for labour (Dʟᵢ):
Dʟᵢ = f(W/P)
This relationship tells us that a firm’s demand for labour will be an inverse function of the real wage: the lower the real wage the more labour will be profitably employed.
In the above analysis we considered the behaviour of an individual firm. The same reasoning can be applied to the economy as a whole. Since the individual firm’s demand for labour is an inverse function of the real wage, by aggregating such functions over all the firms in an economy we arrive at the classical postulate that the aggregate demand for labour is also an inverse function of the real wage.
The aggregate labour demand function is expressed in the equation below:
Dʟ = f(W/P)
The condition for profit maximization is met at the point where the real wage (W/P) is equated with the MPL. If the real wage is 8, then the firm will maximize profits by hiring 3 workers because the MPL is 8.0. This is shown at point D on the graph of the demand for labour, MPL.
In order to get the firm to hire more labour, the real wage must fall because the additional output produced by each additional worker is declining.
At a quantity of labour below 3, say 2, the MPL (=10) exceeds the real wage (8.0). The payment to the worker in real terms is less than the real product produced. Profits will be increased by hiring additional units of labour.
Alternatively, at quantities of labour input above 3, if the real wage is 8, the real wage is above the MPL. The payment to labour exceeds the real product of the marginal worker, and marginal cost exceeds product price. The firm will reduce labour to increase profit.
Thus, the profit-maximizing quantity of labour demanded by a firm at each real wage is given by the labour input that equates the real wage and the MPL. The marginal product of labour curve is the firm’s demand curve for labour.
The implication is that labour demand depends inversely on the level of the real wage. The labour demand curve is downward sloping due to the law of diminishing returns. The higher the real wage, for example, the lower the level of labour input that will equate the real wage to the MPL. In the Figure above, if the wage were 5, instead of 8, labour demand would be 4 instead of 3.
The demand curve for labour is an economy wide aggregation of the individual firms’ demand curves. For each real wage, this curve will give the sum of the quantities of labour input demanded by the firms in the economy. We write this aggregate labour demand function (Dʟ) as: Dʟ = f(W/P) (-)
In the aggregate, as with individual firms, an increase in the real wage lowers the demand for labour.
Employment Determination — Labour Supply
Labour services are supplied by individual workers. Classical economists assumed that the individual attempts to maximize utility (or satisfaction). The level of utility depends positively on both real income, which gives the individual command over goods and services, and leisure.
However, there is a trade-off between the two goals because income is increased by work, which reduces available leisure time.
In other words, how much labour is supplied for a given population depends on households’ preferences for consumption and leisure, both of which yield positive utility. But in order to consume, income must be earned by replacing leisure time with working time. Work is viewed as yielding disutility. Hence the preferences of workers and the real wage will determine the equilibrium amount of labour supplied.
Consider, for example, how individual j allocates one 24-hour period between leisure hours and hours worked. The Figure below illustrates the choice facing the individual:
On the horizontal axis, we measure hours of leisure per day. The maximum, of course, is 24 hours. The horizontal intercept, where the individual chooses no labour and all leisure, is 24. Therefore, the number of hours worked are, 24 minus the number of hours of leisure selected.
Real income is measured on the vertical axis and is equal to the real wage, W/P, multiplied by the number of hours the individual works. Each vertical intercept is the real wage multiplied by 24 hours in the day, which would occur if the individual chose all labour and zero leisure (W/P * 24).
The curved lines in the graph (labeled U₁, U₂, U₃) are indifference curves. Points along one of these curves are combinations of income and leisure that give equal satisfaction to the individual. Hence, the person is indifferent about which point along a given curve is selected.
The slope of the indifference curve gives the rate at which the individual is willing to trade off leisure for income; that is, the increase in income the person would have to receive to be just as well off after giving up a unit of leisure.
In fact, the cost of choosing each hour of leisure is the real wage, W/P, because the individual is choosing not to work for each hour of leisure.
In addition, all points along U₂ for example, yield greater satisfaction to the individual than any point on U₁ because any point on an indifference curve that sits farther to the right indicates a larger income, given leisure (or the same number of hours worked). Therefore, the individual attempts to achieve the “northernmost” possible indifference curve. The higher the real wage, the higher the satisfaction the individual can select (represented by an indifference curve that sits farther to the right).
The straight-line rays originating at the point of 24 hours on the horizontal axis give the budget lines facing the individual. Starting from 24 hours (no work, all leisure), the individual can trade off leisure for income at a rate equal to the hourly real wage, W/P.
The slope of the budget line is the real wage. The higher the real wage, the steeper the budget line, reflecting the fact that at a higher real wage, an individual who increases hours of work by 1 unit (moves one unit to the left along the horizontal axis) will receive a larger increase in income (move farther up the vertical axis along the budget line) than he or she would have received at the lower real wage.
Notice that at a higher real wage, the individual can choose an indifference curve that yields greater satisfaction.
The individual’s labour-leisure choice acts as follows: The individual will supply labour up to the point where the rate at which labour may be traded for leisure in the marketplace, which is given by the real wage (W/P) and is equated with the rate at which the individual is willing to trade labour (give up leisure) in return for income, which is measured by the slope of the individual’s indifference curves (U₁, U₂, U₃).
- Point A: At a real wage of 2.0, the individual will choose 18 hours of leisure. Hours of work chosen will then be 6 (24 hours — 18 hours leisure). This corresponds to point A on the labour supply curve.
- Point B: At a real wage of 3.0, the individual will choose 16 hours of leisure. Hours of work chosen will then be 8. This corresponds to point B on the labour supply curve.
- Point C: At a real wage of 4.0, the individual will choose 15 hours of leisure. Hours of work chosen will then be 9. This corresponds to point C on the labour supply curve.
We construct the labour supply curve for the jth individual based on the choices above. This supply curve consists of points such as A, B, and C, giving the amount of labour the individual will supply at each real wage.
Then the aggregate labour supply curve can be written as:
Sʟ = g(W/P)
Two features of the classical labour supply theory require further comment:
1. The Role of Real Wage First, the wage variable is the real wage. Labour supply is determined by the real wage, not the money wage. The worker receives utility ultimately from consumption, and in making the labour-leisure decision, the individual is concerned with the command over goods and services received for a unit of labour.
Clearly, as the real wage increases (decreases), leisure decreases (increases), and hours of work increase (decrease). Because the real wage (W/P) is measured along the vertical axis on the labour supply curve, if either the money wage or price (or both) change, the number of hours worked are determined by moving along the labour supply curve.
2. The Slope of the Curve (Substitution vs. Income Effect) Second, the labour supply curve is positively sloped; more labour is assumed to be supplied at higher real wage rates. This relation reflects the fact that a higher real wage rate means a higher price for leisure in terms of foregone income. At this higher price, we assume that the worker will choose less leisure.
A rise in the real wage makes leisure more expensive in terms of forgone income and will tend to increase the supply of labour. This is known as the substitution effect. This effect is analogous to the substitution effect in the theory of consumer demand.
There is another effect: the equivalent of the income effect in consumer demand theory. As the real wage increases, the worker is able to achieve a higher level of real income. At higher levels of real income, leisure may become more desirable relative to further increments in income. In other words, a rise in the real wage also makes workers better off, so they can afford to choose more leisure. This is known as the income effect.
With successive increases in the real wage, a point may be reached at which the worker chooses to supply less labour as the real wage increases and consumes more leisure. At this point, the income effect outweighs the substitution effect; the labour supply curve assumes a negative slope and bends back toward the vertical axis (backward-bending supply curve).
However, we will assume that for wage rates observed in industrialized nations, the aggregate labour supply curve does have a positive slope. The classical model assumes that the substitution effect dominates the income effect so that the labour supply responds positively to an increase in the real wage.
In the classical model, the determination of output and employment relies on three core relationships:
Aggregate Production Function:
- Y = AF(K, L)
Labour Demand:
- Dʟ = f(W/P)
Labour Supply:
- Sʟ = g(W/P)
The Equilibrium Condition
Equilibrium occurs when the demand for labour equals the supply of labour (Dʟ = Sʟ). At this point:
- Endogenous Variables: Output, employment, and the real wage are determined. (Note: An endogenous variable is one that is determined within the model itself).
Graphical Determination
The relationship between the labour market and production is illustrated in two steps:
- Step 1 (Graph b): The equilibrium level of employment (Lₑ) and the equilibrium real wage ((W/P)ₑ) are determined at the point of intersection between the aggregate labour demand and labour supply curves.
- Step 2 (Graph a): This determined equilibrium level of labour input (Lₑ) is then mapped onto the production function to determine the equilibrium level of output (Yₑ).
Equilibrium Output and Employment
The determination of the competitive equilibrium output and employment in the classical model occurs where the forces of demand and supply establish an equilibrium market-clearing real wage ((W/P)ₑ) and an equilibrium level of employment (Lₑ).
Output, employment, and the real wage are designated as the endogenous variables in the model, where an endogenous variable is one that is determined within the model.
- Aggregate Production Function: Y = AF(K, L)
- Labour Demand: Dʟ = f(W/P)
- Labour Supply: Sʟ = g(W/P)
When Dʟ = Sʟ: Output, employment, and the real wage are determined. The equilibrium level of labour input (Lₑ) results in an equilibrium level of output (Y) given by the production function.
- Excess Demand: If the real wage were lower than equilibrium, such as (W/P)₂, then there would be excess demand for labour and money wages would rise in response to the competitive bidding of firms, restoring the real wage to its equilibrium value.
- Excess Supply: If the real wage were above equilibrium, such as (W/P)₁, there would be an excess supply of labour. In this case, money wages would fall until the real wage returned to (W/P)ₑ.
This result is guaranteed in the classical model because the classical economists assumed perfectly competitive markets, flexible prices-wages and full information (perfect knowledge).
The level of employment in equilibrium (Lₑ) represents “full employment”, in that all those members of the labour force who desire to work at the equilibrium real wage can do so.
The schedule Sʟ shows how many people are prepared to accept job offers at each real wage whereas the schedule Lᴛ indicates the total number of people who wish to be in the labour force at each real wage rate. Lᴛ has a positive slope, indicating that at higher real wages more people wish to enter the labour force.
In the classical model, labour market equilibrium is associated with unemployment equal to the distance between total labor force and equilibrium employment (voluntary unemployment).
Classical full employment equilibrium is perfectly compatible with the existence of frictional and voluntary unemployment, but does not admit the possibility of involuntary unemployment!
Once the equilibrium level of employment is determined in the labour market, the level of output is determined by the position of the aggregate production function. Lₑ amount of employment will produce Yₑ level of output.
Changes in the equilibrium values can obviously come about if the labour demand curve and/or the labour supply curves shift.
- Technological Change: An upward shift of the production function due to technological change would move the labour demand curve to the right. Providing the labour supply curve has a positive slope, this will lead to an increase in employment, output and the real wage.
- Population Growth: Population growth, by shifting the labour supply curve to the right, would increase employment and output but lower the real wage.
We have seen in the analysis above that competition in the labour market ensures full employment in the classical model. At the equilibrium real wage, no person who wishes to work at that real wage is without employment. In this sense “the classical postulates do not admit the possibility of involuntary unemployment” (Keynes, 1936).
However, the classical economists were perfectly aware that persistent unemployment in excess of the equilibrium level was possible if artificial restrictions were placed on the equilibrating function of real wages. If real wages are held above equilibrium by trade union monopoly power or minimum wage legislation, then obviously everyone who wishes to work at this real wage will not be able to do so.
For classical economists the solution to such “classical unemployment” was simple and obvious: Real wages should be reduced by cutting the money wage.
For Keynes, full employment equilibrium was a “special case” which was not typical of the “economic society in which we actually live”. The full employment equilibrium of the classical model was a special case because it corresponded to a situation where aggregate demand was just sufficient to absorb the level of output produced.
Keynes objected that there was no guarantee that aggregate demand would be at such a level. The classical economists denied the possibility of a deficiency of aggregate demand by applying “Say’s Law” which is “equivalent to the proposition that there is no obstacle to full employment”.
The Determinants of Output and Employment in the Classical Model
In the classical model, the factors that determine output and employment are those factors that determine the positions of the labour supply and demand curves and the position of the aggregate production function.
The production function is shifted by technical change that alters the amount of output forthcoming for given input levels. The production function also shifts as the capital stock changes over time.
The labour demand curve is the MPL curve, the slope of the production function. Consequently, the position of the labour demand curve will shift if the productivity of labour changes because of technical change or capital formation.
From the derivation of the labour supply curve, one can see that this relationship would change as the size of the labour force changes. For example, population growth would shift the labour supply curve out to the right. The labor supply curve would also shift with changes in individuals’ preferences regarding labour-leisure trade-offs.
In other words, exogenous factors are the shifting parameters for the production function, labour demand and labour supply curves. A common feature of the factors determining output in the classical model is that all are variables affecting the supply side of the market for output. In the classical model, the levels of output and employment are determined solely by supply-side factors.
Labor Market Equilibrium: Labour market equilibrium occurs at the real wage (W/P)₀ at equilibrium point A. In the aggregate, labour supply equals labour demand:
- Nᵈ(Dʟ) = Nˢ(Sʟ) Equilibrium employment is N₀.
Output Determination: Substitution of equilibrium employment into the production function determines equilibrium aggregate output, Y₀.
- Y = F(K, N)
Because the supply-determined nature of output and employment is a crucial feature of the classical system, it is worthwhile to demonstrate this property more formally. In order to see that, we consider the features of the labour supply and demand functions more closely.
We can analyze labour supply and demand curves as functions of the real wage versus the nominal (money) wage (W).
1. Labor Supply and Demand as Functions of the Real Wage Equilibrium employment occurs where labour supply equals labour demand based on the real wage (W/P).
2. Labor Supply and Demand as Functions of the Money Wage When labour supply and demand are plotted as functions of the money wage:
- Increases in the price level (from P₁ to 2P₁, then to 3P₁) shift the labour supply and demand schedules upward proportionately.
- The money wage rises proportionately with the price level (from W₁ to 2W₁, then to 3W₁).
- The real wage and level of employment are unchanged.
For labour supply, we can draw a positively sloped curve such as Nˢ(P₁), which gives the amount of labour supplied for each value of the money wage, given that the price level is P₁. The curve is upward-sloping because at the given price level a higher money wage is a higher real wage.
Workers are interested in the real wage, so each price level will have a different curve. For a given money wage each price level will mean a different real wage and, hence, a different amount of labour supplied.
At a price level of 2P₁ or twice that of P₁, the labour supply curve shifts to Nˢ(2P₁); less labour is supplied for any money wage because at the higher price level a given money wage corresponds to a lower real wage. A rise in the price level shifts the labour supply schedule (plotted against the money wage) upward to the left.
That the individual worker is interested only in the real wage can be seen from the fact that the same level of labour (N₁) is supplied at a money wage of W₁ and a price level of P₁ (real wage = W₁/P₁) as at money wage and price combinations of (2W₁, 2P₁) or (3W₁, 3P₁) (real wage = W₁/P₁ at both points). Equiproportional increases (or decreases) in both money wages and the price level leave the quantity of labour supplied unchanged.
Now consider the labour demand curve plotted against the money wage. We know that the labour demand and MPL (Marginal Product of Labour) schedules are equivalent. The condition met at all points along the labour demand curve is:
W/P = MPL
If we want to know the quantity of labour that will be demanded at any money wage, as was the case for the quantity supplied, the answer depends on the price level. Given the money wage, the firm will choose the level of employment at which:
W = MPL · P
This equation has a simple interpretation. For profit maximization, the money wage paid to the additional worker (W) must just equal the worker’s contribution to the firm’s revenue. The worker’s contribution to money revenues equals his or her marginal product multiplied by the product price (MPL · P), which is termed the marginal revenue product of labour (MRPL).
At successively higher price levels (P₁, 2P₁, 3P₁) the labour demand curve plotted against the money wage shifts to the right (from MPL · P₁ to MPL · 2P₁ to MPL · 3P₁).
For a given money wage, more labour is demanded at higher price levels because that money wage corresponds to a lower real wage rate. The demand for labour depends on the real wage. Equiproportional increases in the money wage and the price level from (W₁, P₁) to (2W₁, 2P₁) and (3W₁, 3P₁) leave labour demand unchanged at level N₁. They leave the real wage unchanged at W₁/P₁.
Classical Aggregate Supply Function
From the information regarding the labor market, we can construct the classical aggregate supply function — a relationship that makes clear the supply-determined nature of output in the classical model.
The aggregate supply curve is the macroeconomic analog to the microeconomic concept of the firm’s supply curve. For the firm, the supply curve gives the output forthcoming at each level of the product price.
As we have seen, for the perfectly competitive firm, profits are maximized where marginal cost (W/MPLᵢ for the ith firm) equals product price (P), or equivalently, where the marginal product of labour equals the real wage:
MPLᵢ = W / P
- Individual Firm (Upward Sloping): The individual firm takes the money wage as given in deciding on the optimal output to supply and therefore the quantity of labour to hire. One firm would not expect its effort to hire more labour to cause the money wage to change because the firm is a small part of the overall market. Because the money wage is assumed to be fixed, the output supply curve for the firm is positively sloped. Higher prices mean lower real wages; consequently, the firm demands more labour and produces more output.
- Aggregate Economy (Vertical): In constructing the aggregate supply curve for the economy, we cannot assume that the money wage remains fixed as output and labour input are varied. The money wage must adjust to maintain equilibrium in the labour market. With this important difference, the aggregate supply curve addresses the same question as its microeconomic analog: How will the level of output supplied vary when we change the product price?
Constructing the Classical Aggregate Supply Function
Consider output supplied at three successively higher price levels: P₁, 2P₁, and 3P₁.
Step 1: Initial State At price level P₁ and money wage W₁, employment was N₁ and we assume that the resulting output is Y₁.
Step 2: The Effect of a Price Increase (P₁ → 2P₁) How will output supplied vary as we go to a price level of 2P₁?
- Initial Reaction: At a price level of 2P₁, if the money wage remained at W₁, labour demand would increase to N₂. The higher price would mean a lower real wage, and firms would try to expand both employment and output.
- Labor Market Adjustment: However, the money wage will not remain at W₁. At a price level of 2P₁, the labour supply curve will have shifted. At a money wage of W₁, labour supply will be only N₂’ units.
- The Adjustment Process: There will be an excess demand for labour equal to (N₂ — N₂’) units. The process at work here is one of some firms responding to higher prices by attempting to expand employment and production. To expand employment, they raise nominal wages in an effort to bid workers away from other firms. Firms that lag in the process of raising nominal wages suffer higher quit rates and lose workers. This process of rising nominal wages will stop only when the nominal wage has increased sufficiently to re-equilibrate supply and demand in the labour market.
Step 3: Re-equilibration Re-equilibration occurs at a money wage of 2W₁ where the money wage has increased proportionately with the price level. At this point, the initial real wage is restored, and employment is back at its original level.
Consequently, output supplied at price level 2P₁ is equal to Y₁, the same output level for price level P₁. At a still higher price level of 3P₁, the money wage rises to 3W₁ but again, output is unchanged at Y₁.
The Vertical Aggregate Supply Curve
The aggregate supply curve is vertical.
Higher prices provide an incentive for higher output only if they are not matched by proportionately higher money wages — only if they lower the real wage. However, given the assumptions we have made, equilibrium in the labour market requires that nominal wages rise proportionately with prices to maintain the equilibrium real wage in that market.
The vertical classical aggregate supply curve reflects the fact that higher values of the price level require proportionately higher levels of the money wage for labour market equilibrium. The real wage, employment, and therefore level of output are the same at P₁, 2P₁, and 3P₁. This illustrates the supply-determined nature of output in the classical model.
Factors That Do Not Affect Output In The Classical Model
Which factors will not affect output and employment in the classical model?
Since output and employment are supply determined, the level of aggregate demand will have no effect on output and employment.
- Demand-Side Factors: Factors such as the quantity of money, level of government spending, and level of demand for investment goods by the business sector are all demand-side factors that have no role in determining output and employment.
- Tax Policy: The case of government tax policy is more complex. Changes in taxes, to the degree that they affect the demand side, will not affect output or employment. But changes in tax rates also have incentive or supply-side effects that do matter for output and employment.
Summary
The striking feature of the classical model is the supply-determined nature of output and employment. This property follows from the vertical aggregate supply curve.
The classical aggregate supply curve is vertical because of the assumptions we have made about the labour market. In general, the labour and product markets can be characterized by the term auction market. Labour and output are assumed to be traded in markets that are continually in equilibrium and in which all participants make decisions based on announced real wage rates and product prices.
Especially, two assumptions implicit in this classical representation of the labour market are as follows:
- Perfectly Flexible Prices and Wages: Both prices and nominal wages are perfectly flexible in the short run.
- Perfect Information: Both suppliers and purchasers of labour must know the relevant trading prices. This condition requires that when selling and buying labour at a given money wage (W), both workers and employers know the command over commodities that will result from such a wage (W/P).
These two assumptions, essential for the nature of the classical equilibrium theory of employment and output, are the elements of the classical theory that Keynes attacked.
SAY’S LAW: “Every Supply Creates Its Own Demand”
Say’s Law was put forward by Jean-Baptiste Say in his book Treatise of Political Economy that was published in 1803. According to the simplest version of the law, labour will only offer itself for employment in order to obtain income which is then used to purchase the output produced.
In his own words, Jean-Baptiste Say explains the proposition in the following way:
“A product is no sooner created, than it, from that instant, affords a market for other products to the full extent of its own value… the mere circumstance of the creation of one product immediately opens a vent for other products.” (Say, 1821)
In other words, since the act of production simultaneously creates income and purchasing power, there could be no obstacle to full employment caused by a deficiency of aggregate demand. The dictum “supply creates its own demand” captures the essence of Say’s Law and characterizes the essential feature of exchange within a specialized economy.
The Classical View
That the act of supply created an equivalent demand seemed obvious to the classical writers. The law does not deny the possibility that a misallocation of resources can occur and that an oversupply of certain commodities can develop. But this problem would be temporary, and no such excess supply could occur for goods as a whole.
Say’s Law was originally set forth in the context of a barter economy where the act of supplying one good unavoidably implies the demand for some other good. In general, classical economists, notably Ricardo and Mill, gave support to Say’s Law. They believed that it would also be true for a monetary exchange economy. Because for classicals, money was nothing more than a convenient medium of exchange which enabled market participants to avoid the awkwardness and inconvenience of barter.
If Say’s Law applies to a money-using economy, it implies that a market is guaranteed for whatever level of output is produced, although market forces will obviously lead to changes in the composition of aggregate output. If aggregate demand and aggregate supply are always equal, then money is nothing more than a “veil” covering the underlying real forces in the economy.
At this point it is important to distinguish between two versions of Say’s Law:
- The Weak Version: It implies that each act of production and supply necessarily involves the creation of an equivalent demand for output in general. But this version of Say’s Law does not guarantee that the output produced will be consistent with full employment. It merely states that whatever level of aggregate output happens to be forthcoming will find a market. This applies to both depressed (low) and buoyant (high) levels of output.
- The Strong Version: This version states that in a competitive market economy there will be an automatic tendency for full employment to be established. It implies an equality of aggregate demand and supply which is consistent with labour market equilibrium (demand for labour = supply of labour) and with full employment. It is equivalent to the proposition that there is no obstacle to the achievement of full employment in terms of a deficiency of aggregate demand.
The Classical Theory of Interest Rate Determination
To see how the classical economists justified their belief that aggregate spending in the economy will always be sufficient to purchase the full employment level of output, we need to examine their ideas relating to investment, saving and the rate of interest.
The working of Say’s Law is closely related to the interest rate determination in the classical model. The classical theory of interest rate determination plays a crucial role in ensuring that a deficiency of aggregate demand does not occur.
In the classical system, the components of aggregate demand — consumption, investment, and government spending — play their explicit role in determining the interest rate. It is, in fact, the interest rate that guarantees that exogenous changes in the particular components of demand do not affect aggregate demand.
If we imagine an economy consisting of two sectors, firms and households, we can write down the following equation, which tells us that in equilibrium aggregate expenditure (E) must equal aggregate output (Y):
E = C(r) + I(r) = Y
According to the equation above, aggregate expenditure (demand) consists of two components: Investment expenditure (I) which arises from firms and consumption expenditure © which arises from households.
The planned demand for goods (E) is the sum of the planned demand for consumption goods plus the planned demand for investment goods. In the classical model, the demand for both types of goods is a function of the interest rate (r).
Since households do not automatically spend all of their income, we can also write down the equation below:
Y — C(r) = S(r)
Combining the two equations above yields the equilibrium condition:
S(r) = I(r)
Then in the classical model saving (S) is also a function of the interest rate. The higher the rate of interest the more willing will savers be to replace present consumption with future consumption. Therefore, the classical economists viewed the interest rate as a real reward for abstinence or thrift.
Investment, Saving, and Market Equilibrium
- Saving (Supply of Loanable Funds): The flow of saving represents a supply of loanable funds in the capital market. Since household saving responds positively to the rate of interest (ΔS/Δr > 0), household consumption must be negatively related to the rate of interest (ΔC/Δr < 0).
- Investment (Demand for Loanable Funds): Investment expenditure on capital goods is negatively related to the rate of interest in the classical model (ΔI/Δr < 0) and represents a demand for loanable funds in the capital market.
- Logic: Investment spending by firms can only be justified if the expected rate of return from the expenditure is greater than, or at least equal to, the cost of acquiring the funds used to purchase the capital goods. The higher the rate of interest, the higher the explicit (and implicit) cost of the funds used to purchase the capital goods.
Supply of Loanable Funds & Demand for Loanable Funds
The classical theory says that when investment expenditures of firms (demand for loanable funds) are equal to savings of households (supply of loanable funds), the equilibrium interest rate is determined in the capital (or loanable funds) market.
More clearly, the equilibrium interest rate in the classical theory is the rate at which the amount of funds individuals desire to lend is just equal to the amount others desire to borrow.
- Borrowing: Consists of selling a standard bond, a promise to pay certain amounts in the future.
- Lending: Consists of buying such bonds.
In the classical system, the suppliers of bonds (borrowers) are:
- Firms, which finance all investment expenditures by the sale of bonds.
- The Government, which might sell bonds to finance spending in excess of tax revenues (G — T).
The Demand for Loanable Funds (Supply of Bonds)
In the classical model, the level of business investment is a function of the expected profitability (expected rate of return) of investment projects and the rate of interest.
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The expected profitability of investment projects is assumed to vary with expectations of product demand over the life of these projects, and the state of these expectations is subject to exogenous shifts. Investment expenditures vary inversely with the interest rate for a given expected profitability.
- The rate of interest represents the cost of borrowing funds to finance these investment projects.
- At a high interest rate, fewer projects will be profitable.
- At successively lower rates of interest (lower borrowing costs), more and more projects will become profitable and investment will increase.
The Government Role The level of the government deficit (excess of spending over revenues: G — T), as well as the portion of the deficit the government might choose to finance by selling bonds to the public, are exogenous policy variables. Thus, on the supply (borrowing) side of the bond market, the government bond supply is exogenous.
Total Demand for Funds The supply of bonds by firms equals the level of investment expenditure. Then, government and firms supply bonds and demand funds in the loanable funds (or capital) market.
The Supply of Loanable Funds (Demand for Bonds)
On the demand (lending) side of the bond market are the individual savers (households) who purchase the bonds. In the classical model, saving is taken to be a positive function of the rate of interest.
The act of saving is the act of forgoing current consumption to have a command over goods in a future period — a trade-off of current consumption for future consumption.
- As the interest rate increases, the terms of the trade-off become more favorable.
- Classical economists assume that individuals will take advantage of this more favorable trade-off. They will save more at higher rates of interest.
Note on Money vs. Bonds: Although money is also a potential store of wealth, because money pays no interest, classical economists assume that bonds will be preferred as a store of wealth. Classical economists believe that people may shift their wealth into the form of money in times of severe economic conditions. But in normal times the classical assumption is that saving is a demand for bonds.
The equilibrium interest rate (r₀) is the rate that equates the supply of loanable funds, which consists of saving (S) of households, with the demand for loanable funds, which consists of investment (I) of firms plus the bond-financed government deficit (G — T).
Equilibrium Equations:
E = C(r) + I(r) + G = Y Y — C(r) = S(r) S(r) = I(r) + (G — T)
Where:
- Supply of Loanable Funds (Demand for Bonds): S(r)
- Demand for Loanable Funds (Supply of Bonds): I(r) + (G — T)
The Classical Interest Rate Mechanism and Say’s Law
In the classical model, variations in the interest rate act as an equilibrating force which maintains equality between the demand for and supply of loanable funds, ensuring that aggregate demand is never deficient.
The flexibility in the interest rate is crucial to the classical equilibration process and to the working of Say’s Law.
Scenario 1: Households Decide to Save More (Consume Less)
Let’s see the importance of interest rate flexibility by asking what would happen if households suddenly decided to save more (consume less):
- This causes a rightward shift of the saving function (from S₀ to S₁).
- The initial excess supply of loanable funds leads to a fall in the rate of interest from r₀ to r₁.
- This fall in interest rates would encourage an increase in investment expenditure from I₀ to I₁.
Result: Since E₀ — I₀ equals consumption expenditure, it is clear that the rise in investment expenditure (I₁ — I₀) exactly offsets the fall in consumption expenditure. Aggregate expenditure would remain at E₀ although its composition would change.
E = C + I = Y -ΔC = +ΔI
Graphically, point A corresponds to the strong version of Say’s Law. Not only are aggregate expenditure and output in equality, Yₑ corresponds to the level of output associated with full employment labour market equilibrium.
Scenario 2: Autonomous Decline in Investment Demand
Consider the effect of an autonomous decline in investment demand as a result of a decrease in expected profitability.
- An autonomous decline in investment shifts the investment schedule to the left from I₀ to I₁ (by distance ΔI).
- The supply of loanable funds exceeds demand for loanable funds and puts downward pressure on the rate of interest.
- The equilibrium interest rate declines from r₀ to r₁.
As the interest rate falls, two adjustments occur:
- Adjustment A: Saving declines; thus, consumption © increases. The amount of this decline in saving and the equal increase in current consumption is given by distance A.
- Adjustment B: Investment is revived by the decline in the interest rate. This interest-rate-induced increase in investment is measured by distance B.
Result: The interest rate-induced increases in consumption and investment just balance the autonomous decline in investment.
-ΔI = +ΔC (= -ΔS) + ΔI (Distance A + Distance B) = Original Decline
Then, the total aggregate demand (E = C + I) does not change; only its composition changes. SAY’S LAW WORKS!
Conclusion: The Stabilizing Role of Interest Rates
This stabilizing role of the interest rate is important to the classical system. The interest-rate adjustment mechanism supports the classical argument on full employment.
The perfectly flexible interest rate mechanism shows that Say’s Law is valid: Supply creates demand and aggregate demand never becomes deficient.
Shocks that affect consumption demand, investment demand, or government demand will not affect the demand for output as a whole. These shocks will not shift the aggregate demand curve; only the components of aggregate demand change. The aggregate demand will change if only aggregate supply changes.
Classical vs. Keynesian View
Even though in the classical model the decisions to save and invest can be carried out by different sets of people, the rate of interest will change to reconcile the desires to save and invest.
- Keynesian Model: Divergences between S and I cause a quantity response. In the case of an increase in saving, the Keynesian model predicts a decline in aggregate spending, output, and employment (Keynes’s “Paradox of Thrift”).
- Classical Model: Armed with Say’s Law, flexible wages, prices, and the interest rate, the economy can experience changes in the structure (components) of aggregate demand but no prolonged demand deficiency and involuntary unemployment.
Historical Note: Not all the classical economists accepted Say’s Law and its implications. Robert Thomas Malthus argued that a general excess supply of commodities was possible. However, David Ricardo, John Stuart Mill, and the followers of Jean-Baptiste Say believed that the conditions of supply determine aggregate output.
Malthus, anticipating John Maynard Keynes, gave emphasis to demand as the determining factor of supply. For this reason, Keynes praised Malthus for anticipating his own ideas with respect to a general deficiency of aggregate demand. Malthus, like Keynes, was more concerned with the short run whereas Ricardo and other classical economists concentrated on the long run.
The Quantity Theory of Money
In our analysis of the classical model, we have concentrated on the real sector so far. The operation of the labour, product and capital markets, supported by Say’s Law, provided the classical economists with a theoretical system capable of explaining the determination of the real variables in the system.
But what determines the price level in the classical model?
The final component that explains the determination of the price level and the other nominal variables in the classical economists’ system is the quantity theory of money. Therefore, to understand the determination of the price level in the classical system, we analyze the role of money.
In the classical theory, the quantity of money determines aggregate demand, which in turn determines the price level.
The important feature of classical macroeconomic theory is the separation of real and nominal variables. This classical dichotomy enables us to examine the behaviour of the real variables in the economic system while ignoring the nominal variables.
In the classical model, the quantity of money does not play any role in the determination of the real variables. The neutrality of money is a crucial property of the classical model.
To explain the determination of the nominal variables in the system, the classical economists applied to the quantity theory of money.
A long line of famous economists have either contributed to the development of this theory or have been associated with its policy prescriptions. The list includes Richard Cantillon, David Hume, David Ricardo, John Stuart Mill, Alfred Marshall, Irving Fisher, Arthur C. Pigou, Friedrich Hayek and even John Maynard Keynes.
More recently the quantity theory of money has been associated with the development of monetarism and the work of Milton Friedman. However, the quantity theory of money was well established in classical macroeconomics following the publication of David Hume’s influential essay, Of Money, in 1752.
There are two highly influential versions of the quantity theory of money in the literature:
- The Equation of Exchange: Associated with Irving Fisher.
- The Cambridge Cash-Balance Approach: Associated with Alfred Marshall and Arthur C. Pigou.
1.The Equation of Exchange (Irving Fisher)
The starting point for the classical quantity theory of money is the equation of exchange, which belongs to the American quantity theorist Irving Fisher. It is an identity relating the volume of transactions at current prices to the supply of money times the turnover rate of each unit of money.
The Transactions Version:
M Vₜ ≡ Pₜ T
Where:
- M: Quantity of money
- Vₜ: Transactions velocity of money (turnover rate)
- Pₜ: Price index for the items traded
- T: Volume of transactions
Transactions velocity of money (Vₜ) measures the average number of times each unit of money is used in transactions during a given period. This relationship is an identity because of the ex-post definition of velocity (Vₜ ≡ PₜT / M).
The Income Version: Another expression of the equation of exchange focuses only on income transactions: MV ≡ PY
Where:
- M: Quantity of money
- V: Income velocity of money (average number of times a unit of money is used in a transaction involving current output).
- P: Price index for currently produced output.
- Y: Level of current output (Real GDP).
We focus on this form of the equation because the variables are easier to measure and are central to our concerns.
Determination of the Price Level
Fisher and other quantity theorists assume that the equilibrium values of the elements in the equation of exchange, with the exception of the price level, are determined by other forces. Thus, the equation of exchange determines the price level.
Assumptions:
- Money Supply (M): Exogenously determined by the monetary policy authority.
- Output (Y): Supply determined (fixed at full employment level).
- Velocity (V): Determined by the payment habits and payment technology of society (e.g., length of pay period, use of credit). It is regarded as fixed for the short run.
The Result: With output fixed (Y) and velocity fixed (V), the equation of exchange expresses a relationship of proportionality between the exogenously given money supply and the price level:
MV = PY or P = MV / Y
The bar over the V and Y indicates that these terms can be taken as given. With V and Y constant, it is easy to see that P depends on M and that ΔM equals ΔP.
The price equation indicates the dependence of the price level on the supply of money. A doubling of M doubles P, or a 10 percent increase in M leads to a 10 percent increase in P.
This is the basic result of the quantity theory of money: The quantity of money determines the price level.
2. The Cambridge Cash-Balance Approach
How do changes in the money supply affect the price level? This question can be answered more easily by the Cambridge approach to the quantity theory of money. The equation of exchange does not fully explain this process.
The Cambridge approach, named after Cambridge University, belongs to Alfred Marshall and A. C. Pigou. It also demonstrates a proportional relationship between the quantity of money and the aggregate price level. However, the foundation of this relationship is less mechanistic than the transactions version of the quantity theory of Irving Fisher.
The Cambridge economists drew a clear distinction in their version of the quantity theory between the demand for money (Mᵈ) and the supply of money (M). This approach focuses on the demand for money:
Mᵈ = kPY
In this approach, money demand (Mᵈ) is assumed to be a proportion (k) of nominal income, which is the price level (P) times the level of real income (Y).
Why do people hold money?
- People hold some money because of the convenience that money provides in transactions compared with other stores of value.
- Money also provides security by lessening the possibility of inconvenience or bankruptcy from failing to meet unexpected obligations.
But as Pigou noted, “Currency held in the hand yields no income.” Since the desirable property of money is its usefulness for transactions, the demand for money depends on the level of transactions, which may be supposed to vary closely with income.
Then the only motive to demand for money in the classical model is the transactions motive, and it depends on income.
The proportion of income that would be optimal to hold in the form of money (k) is assumed to be stable in the short run, depending on the payment habits of the society as in the equation of exchange. In other words, k is the fraction of the annual value of nominal national income (PY) that agents (firms and households) wish to hold.
Equilibrium and Relationship to Fisher’s Equation
In equilibrium, the exogenous supply of money must equal the quantity of money demanded:
M = Mᵈ = kPY
With k fixed in the short run and real output (Y) determined by supply conditions, the Cambridge equation also shows the proportional relationship between the price level and the money supply. As in the Fisherian approach, the quantity of money determines the price level.
The formal equivalence of the Cambridge equation and Fisher’s version of the equation of exchange can be seen by rewriting the equation above as:
M (1/k) = PY -> MV = PY
By comparing this with Fisher’s equation (MV = PY), we can see that the two formulations are equivalent, with V equal to 1/k.
Example: If individuals wish to hold an amount equal to one-fourth of the nominal income in the form of money (k = 1/4), the number of times the average dollar is used in income transactions will be four (V = 4).
Although the two formulations of the quantity theory are formally equivalent, the Cambridge version represents a step toward more modern monetary theories because the Cambridge focus is on the quantity theory as a theory of the demand for money.
Summary of Determination: The proportional relationship between the quantity of money and the price level results from the fact that:
- The proportion of nominal income people wished to hold in the form of money (k) is constant.
- The level of real output (Y) is fixed by supply conditions (predetermined at its full employment value by the production function and the labour market).
With k and Y constant, M determines P.
Transmission Mechanism in the Classical Model
In addition, the Cambridge focus on money demand leads to an answer to the question about the way money affects the price level (transmission mechanism).
Let us suppose that we begin at equilibrium and then consider the effects of doubling the quantity of money.
- Disequilibrium: If the money market is initially in equilibrium, then an increase in the money supply creates disequilibrium. There is an excess of money supply over the amount demanded (M > Mᵈ).
- Behavioral Change: Individuals try to reduce their money holdings to the optimal proportion of their income by putting this excess money into alternative uses of consumption and investment. They increase their demand for commodities.
- Price Adjustment: This increased demand for commodities puts upward pressure on prices. In the language of classical economists, there is “too much money chasing too few goods.”
The New Equilibrium If output is unchanged, as it would be in the classical model, and k is constant, a new equilibrium will be reached only after the price level is doubled. At that point, nominal income (PY), and hence money demand (Mᵈ = kPY), will have doubled.
This is the link in the classical system between money and prices; an excess supply of money leads to increased demand for commodities and upward pressure on the price level.
The Classical Aggregate Demand Curve
We can use the quantity theory — equation of exchange — to construct the classical aggregate demand curve. The quantity theory is the implicit theory of the aggregate demand for output within the classical system.
For concreteness, let’s assign numerical values:
- Initially, let the supply of money (M) be 300 units.
- Let the value of k be one-fourth, so that velocity (V) is 4.
For the equation (MV = PY) to hold, nominal income (PY) must be equal to 1,200 (4 × 300).
The aggregate demand curve Yᵈ(M=300) connects all the points where P × Y equals 1,200 units. For example:
- If Real Output (Y) = 300, Price Level (P) = 4.0.
- If Real Output (Y) = 600, Price Level (P) = 2.0.
The classical aggregate demand curve plots combinations of the price level (P) and output (Y) consistent with the quantity theory equation MV = PY for a given money supply (M) and fixed velocity (V).
Now consider a higher value of the money supply, for example, M = 400 units (with V = 4).
- Now, PY must be equal to 1,600.
- The aggregate demand curve Yᵈ(M=400) lies above and to the right of the previous schedule.
Conclusion: An increase in the money supply shifts the aggregate demand curve to the right.
The classical aggregate demand curve plots combinations of the price level (P) and output (Y) consistent with the quantity theory equation MV = PY, for a given money supply (M) and fixed velocity (V). With M = 300 and velocity assumed to be 4, points such as P = 12.0 and Y = 100 or P = 6.0 and Y = 200 (PY = 1,200 = MV in each case) lie along the aggregate demand curve. An increase in the money supply to M = 400 shifts the aggregate demand curve to the right.
The “Implicit” Nature of Classical Aggregate Demand
The classical theory of aggregate demand has been termed an implicit theory. The theory is not explicit in the sense that it focuses on the components of aggregate demand and explains the factors that determine their level.
The components of aggregate demand, such as consumption, investment, or government expenditures, are not shifting parameters for the classical AD curve.
- Why? Because of the interest rate mechanism working in this model (Say’s Law). Changes in the components (e.g., fiscal policy) affect the interest rate and the composition of demand, but not total aggregate demand.
- What shifts AD? The aggregate demand curve shifts only when the money supply changes.
If we combine a downward-sloping aggregate demand curve (for a given money supply) with the vertical aggregate supply curve, we can illustrate the determination of price and output levels in the classical model.
Analysis of Monetary Expansion Consider successive increases in the money supply (M₁ → M₂ → M₃):
- The aggregate demand curve shifts to the right (AD₁ → AD₂ → AD₃).
- The price level rises (P₁ → P₂ → P₃).
- Output remains unchanged: Because the aggregate supply curve is vertical (supply-determined), increases in demand do not affect output. Output remains at the full employment level (Y_F).
For a given value of k (or V), a change in the quantity of money is the only factor that shifts the aggregate demand curve.
Successive increases in the money supply, from M1 to M2 and then to M3 shift the aggregate demand curve to the right, from AD (M1 ) to AD (M2) to AD (M3 ). The price level rises from P1 to P2 to P3 . Output, which is supplydetermined, is unchanged (Y1 = Y2 = Y3 ) at full employment level.
The interaction between the real and monetary sectors illustrates the Classical Dichotomy and the Neutrality of Money.
The 4-Quadrant Model Analysis
Real Sector (Labour & Product Markets):
- A competitive labour market generates equilibrium employment (L₀) and an equilibrium real wage (W₀/P₀).
- From the production function, this employment leads to a full employment output of Y₀.
- The Aggregate Supply (AS) function is perfectly inelastic (vertical).
Monetary Sector (Aggregate Demand):
- The classical AD curve is derived from the equation of exchange (MV = PY).
- With a constant supply of money (M₀) and V, a higher price level must be associated with a lower level of real output.
Suppose the monetary authorities increase the supply of money from M₀ to M₁ to try to increase real output.
Money Market Disequilibrium: The increase in money creates an excess supply of money (M > Mᵈ), leading to an increase in the demand for goods (AD shifts right to AD₁).
Price Adjustment: Since Output (Y) is constrained at Y₀ by the labour market, prices rise to P₁.
Labour Market Adjustment:
- For a given nominal wage (W₀), the rise in prices lowers the real wage to W₀/P₁.
- This creates an excess demand for labour (since labor is cheaper).
- Competitive bidding by employers drives the nominal wage up until it reaches W₁.
Restoration of Equilibrium: The nominal wage rises proportionally to the price level, restoring the real wage to its original value (W₀/P₀ = W₁/P₁).
Irving Fisher also demonstrated how monetary expansion would raise the nominal rate of interest through the “Fisher effect”.
- Real Interest Rate: Adjusts to equate saving and investment in the loanable funds market.
- Nominal Interest Rate: Equals the real interest rate plus the inflation rate.
- Result: Monetary expansion, by raising the rate of inflation, will also raise the nominal interest rate.
The real sector and monetary sector are completely seperated from each other in the classical model because of the neutrality of money.
The result of a monetary expansion is that the price level, nominal income, nominal wages, and the nominal interest rate will increase, but all the real variables in the system remain unaffected.
Money is Neutral: The quantity of money does not affect real variables, such as employment, output, real wage, and real interest rate.
“Tis evident that the greater or less plenty of money is of no consequence since the prices of commodities are always proportional to the plenty of money.” — David Hume (1752)
Policy Implications of The Classical Model
We will analyze the effects of monetary and fiscal policy actions within the classical model. We consider the effects of various policy shifts on output, employment, price level, and interest rate.
Monetary Policy
In the classical system, the quantity of money determines the price level, the level of nominal income, nominal wages, and nominal interest rate.
In this sense, monetary policy is quite important to classical economists. Stable money is a requirement for stable prices.
In another sense, money is not important. The quantity of money does not affect the equilibrium values of the real variables in the system: output, employment, real wages, and the real interest rate. Money is neutral.
The output and employment are determined by supply-side variables. Both markets are always in equilibrium at full employment levels.
The Real Interest Rate The theory of the equilibrium interest rate we have constructed here is a real theory that is not related to the quantity of money. The real interest rate is determined in the loanable funds market. Factors determining the real interest rate are real investment demand, real saving, and the real value of the government deficit — what the classical economists called the forces of “productivity and thrift.”
Monetary policy is ineffective in the classical model. The changes in the amount of money do not affect real variables. Money is neutral. An expansionary monetary policy will result in higher prices, higher nominal wages and higher nominal interest rates.
Fiscal Policy
Let’s consider the effects of an increase in government spending. How is the increased spending financed?
The government has a budget constraint, the condition that all expenditures must be financed from some source. The government has three sources of funds:
- Taxation
- Selling bonds to the public (borrowing funds from the public)
- Creating new money
Then, to increase spending, the government must increase taxation, sell additional bonds to the public, or increase the money supply.
For now, if we assume that the money supply and tax collections are fixed, the increased government expenditures will be financed by selling bonds to the public.
If government spending is greater than tax revenue, then (G — T) is positive, where G is government spending, T is tax revenue, and (G — T) is the government deficit.
We assume that before the increase in government spending the government budget was in balance; that is, (G = T). The government deficit is then equal to the increase in government spending, (G — T)₁.
Market Adjustments:
- Initial Equilibrium: Initially, with no government deficit, the loanable funds market is in equilibrium at point E. At this point, the equilibrium interest rate, r₀, equates the supply of loanable funds with the demand for loanable funds (private investment, I).
- Shift in Demand: If the increase in government spending is financed by selling bonds, then total demand for loanable funds includes both investment (I) and government borrowing ((G — T)₁). The demand for loanable funds curve shifts to the right, from I to I + (G — T)₁, moving from equilibrium point E to equilibrium point F. The distance of the horizontal shift in the curve measures the amount of the increase in government deficit spending.
- Interest Rate Rise: The increase in government spending creates an increased demand for loanable funds as the government sells bonds to the public to finance the new spending. This creates an excess of borrowers over lenders at the initial interest rate r₀ and the interest rate is pushed up to r₁.
The increase in the interest rate has two effects:
- Decrease in Consumption: Saving increases from S₀ to S₁ (distance A). An increase in saving means an equal amount of decline in consumption.
- Decrease in Investment: The quantity of investment declines with the higher interest rate. At r₁, the new level of investment is I₁ (distance B).
The decline in consumption, which equals the amount of increased saving (distance A) plus the decline in investment (distance B), just equals the amount of the increase in government spending (G — T)₁.
The increase in government spending financed by selling bonds to the public pushes the interest rate up by enough to “crowd out” an equal amount of private expenditure (consumption plus investment). This is called the crowding-out effect.
Δ(G — T)₁ = -ΔC (+ΔS) + (-ΔI)
Why does this happen?
- Private expenditures are discouraged because the higher interest rate causes households to substitute future consumption for current consumption — in other words, to save more.
- Investment declines because fewer projects appear profitable with higher borrowing costs (higher interest rate).
It is this crowding out that keeps aggregate demand from increasing when the government expenditures rise.
- Total Aggregate Demand: E = C + I + G = Y. Total aggregate demand does not change; only components change.
- Prices: Increases in government expenditures financed by bonds do not affect the price level since aggregate demand does not change.
- Real Output: Output and employment are not affected by changes in government spending.
If the increase in government spending is financed by printing money, it produces the same effect as an expansionary monetary policy.
Since the quantity of money is changed, the price level will change proportionately. As we have previously analyzed, an increase in the money supply shifts the aggregate demand curve up along the vertical aggregate supply curve and raises the price level.
In the classical system, the source of the increase in the money supply does not matter. A given change in the money supply has the same effect whether it enters the economy to finance an increase in government spending or in another manner. The increase in government spending has no independent effect on aggregate demand.
TAX POLICY: Demand-Side Effects
As long as we consider demand-side effects, a change in taxes produces results that are analogous to those for government spending.
For example, a tax cut stimulates consumption by increasing the disposable income of households. However, the financing method determines the outcome:
Bond-Financed Tax Cut: If the government sells bonds to the public to replace the revenues lost by the tax cut, the same crowding-out process will follow, as in the case of a bond-financed increase in government spending.
- The equilibrium interest rate rises.
- Investment falls.
- There will also be an interest-rate-induced rise in saving, meaning that consumption will fall back toward the pre-tax-cut level.
- Result: In the case of a tax cut, as with an increase in government spending, aggregate demand will not be affected.
Money-Financed Tax Cut: If revenues lost because of the tax cut are replaced by printing new money, then the money creation increases aggregate demand, and the tax cut causes the price level to rise.
- However, the reason for the rise of the price level is the increase in the money supply.
- Result: The tax cut itself does not have an independent effect on aggregate demand.
TAX POLICY: Supply-Side Effects
Suppose the tax cut is in the form of reduced income tax rates (e.g., the marginal income tax rate is cut from 40% to 20%).
In the classical model, such a change will have an incentive effect on labour supply. The change will affect the supply side of the model and will affect output and employment.
The Mechanism A cut in the tax rate increases the labour supply at any value of the pre-tax real wage and shifts the labour supply schedule out to the right. This is because the worker is concerned about the after-tax real wage, which is (1 — tʸ)W/P, where tʸ is the marginal income tax rate.
If we include an income tax, the labour supply function becomes:
Sʟ = g[(1 — tʸ)W/P]
For a given pre-tax real wage (W/P), a cut in the income tax represents an increase in the after-tax real wage and therefore increases labour supply.
Analysis of the Tax Cut (tʸ: 0.40 → 0.20)
- Labour Market: As the marginal income tax rate falls, the labour supply curve shifts to the right. Equilibrium employment increases (e.g., from N₀ to N₁).
- Production Function: The increase in employment leads to an increase in output (from Y₀ to Y₁).
- Aggregate Supply & Demand: This increase in the supply-determined level of output is shown as a shift to the right in the aggregate supply curve (from Yˢ(tʸ=0.40) to Yˢ(tʸ=0.20)).
- Price Level: Because aggregate demand is unchanged (determined by the level of the money supply), this increase in aggregate supply results in a fall in the price level.
In part a , a reduction in the marginal income tax rate (from 0.40 to 0.20) increases the after-tax real wage for a given value of the pre-tax real wage. The labor supply curve shifts to the right. Equilibrium moves from point A to point B. Employment and output increase, as shown in part b of the graph, moving from point A to point B on the production function. This increase in output is represented by the shift to the right in the vertical aggregate supply curve in part c.
Summary of Fiscal Policy
- Demand-Side: Changes in government spending or taxes have no independent effects on aggregate demand because of the interest-rate adjustment and resulting crowding-out effects.
- Supply-Side: Changes in marginal income tax rates have additional supply-side effects. A reduction in the marginal income tax rate stimulates labour supply and leads to an increase in employment and output.
CONCLUSION
Classical economists believe in the self-adjusting tendencies of the economy. For them, the private sector will be stable, and full employment will be achieved without destabilizing government actions.
Two Main Stabilizers:
- Interest Rate: Adjusts to keep shocks to sectoral demands from affecting aggregate demand.
- Flexible Prices and Wages: Keep changes in aggregate demand from affecting output. Flexibility of prices and wages is crucial to the full-employment properties of the classical system.
The inherent stability of the private sector leads classical economists to non-interventionist policy conclusions.
The Classical Dichotomy Another central feature of the classical system is the dichotomy between the factors determining real and nominal variables.
- Real Variables: Determined by real (supply-side) factors.
- Output and employment depend primarily on population, technology, and capital formation.
- The interest rate depends on productivity and thrift.
- Nominal Variables: Money is a “veil” determining the nominal values by which quantities are measured, but monetary factors do not play a role in determining these real quantities.
