*Businesstopia*, January 12, 2018, https://www.businesstopia.net/economics/macro/employment-and-output-determination-under-classical-system.

Classical theory provides an explanation of the labor market along with the analysis of product market and money market. The classical system defines labor demand, labor supply, and production function to determine the process of employment determination.

Before understanding employment and output determination, major assumptions of classical theory should be looked into.

### Assumptions of Classical Theory of Employment

The basic assumptions of the theory include:

- Supply creates its own demand. Sufficient market exists for all the produced goods and services.
- Perfect competition exists in the economy for both product market and factor resource market.
- Market force of demand and supply determine the level of prices in the economy. Individuals are price takers, not price makers.
- Rational self-interest motivates individuals within the market where producers want to maximize profit and consumers want to maximize utility.
- Market tends to self-adjust prices, wages and interest rates to maintain equilibrium in the economy.

### Production Function and Supply of Aggregate Output

Aggregate output in an economy is explained with the help of production function. A production function simply shows the level of output that a firm can produce as a function of inputs to production in the form of labor and capital.

In macroeconomics, aggregate output is a function of labor employed by all firms with a given level of capital and technology. In the short run, some factors like capital goods and technology remain constant. Mathematically,

Where, Y= Real output/GDP; K= Capital input; L= Labor input technology. The bar above a variable denotes the quantity to be fixed.

The production function is graphically represented below:

In the graph, vertical axis measures output and horizontal axis shows variable input i.e. labor in this case. The production function is concave downwards which shows the law of diminishing returns. The law states that output increases as additions are made to the variable factor. The marginal product of variable factors decline with more and more of its use with other fixed factors. This can be expressed as

MP_{L} is the additional output produced as a result of addition in the number of labors.

According to the law of diminishing returns, marginal product of the variable increases, reaches a maximum level and gradually decreases with the increase in the use of variable factor. Due to this, the marginal product curve of labor (MP_{L}), derived from the slope of production function, slopes downward as more labor is added to the existing workforce. Thus,

#### Firm’s Decision

In the classical economic system, the main of the firms is to maximize profit. For this, they have to determine the level of output to be produced and the number of workers to be employed. The demand for labors and other factor resources are determined by the demand for the products in the market. It also depends on the extra unit of output that an additional worker can produce if added to the current workforce.

In order to maximize their profit, firms employ factors of production to the point where marginal product revenue is equal to the marginal factor cost. This means, producers would be willing to contribute until MC_{L }= MR. Here, MC_{L }is the wage paid to the additional labor; MR is the additional revenue generated after the addition of an extra labor.

So, it can be stated that the demand for a factor of production by a firm depends on its marginal product, and the demand curve for the factor is its downward sloping marginal product curve.

Mathematically, profit of a firm cab be expressed as

*Businesstopia*, January 12, 2018, https://www.businesstopia.net/economics/macro/employment-and-output-determination-under-classical-system.

Profit = Total Revenue – Total Cost

π = TR – TC

Also, Total Revenue = P x Y

And, Total Cost = w x L + r x K

Where, w = wage paid for each unit of labor;

L = Total labor employed

r = Average rent paid for capital goods

K = Capital

Replacing TC by ‘w x L + r x K’ we get

π = P x Y – w x L – r x K

Since firms wish to maximize their profit employing labor in addition to the available capital and given technology, we replace output level Y by the production function to see how profit is dependent on factors of production.

The equations shows profit depends on the price of the product (P), wages (w) and rent (r), the factors K and L, and the level of produced commodities

However, in order to determine the number of labors to hire, firms consider the equality between marginal product revenue and marginal factor cost. Firms demand factors on the basis of marginal product contribution (revenue).

The objective of the firm is to maximize profit which is shown by the equation: π = P x Y – w x L – r x K. partially differentiating the equation π = P x f (L, K) – w x L – r x K with respect to L and set it equal to zero as capital is held constant. This is a necessary condition for optimization, therefore,

The partial derivative is set to zero because when a variable is at its maximum or minimum, no change occurs in its value. Market price P and capital stock are fixed in this case, so the focus is on L. Thus,

Δπ/ ΔL= P x Δf/ΔL – w = 0

Here, Δf/ΔL refers to the change in output per unit change in labor termed as ‘marginal product of labor’ that is, Δf/ΔL= MP_{L} and the term P x Δf/ΔL is change in the value of output per unit change in labor termed as ‘marginal value product of labor i.e. MVP_{L}. Explaining these we get, P x MP_{L} – w = 0

From this, we get,

P x MP_{L}

Or MP_{L} = w/P

The two equations have two expressions, where

W= P x MP_{L} shows firms in a competitive market, hire labor up to the point where nominal wage is equal to marginal product of labor (P x MP_{L} = VMP_{L}).

Alternately, the expression w/P = MP_{L} states that in a perfectly competitive market, firms hire labor to the level where real wage is equal to marginal product of labor. These expressions determine the demand curve of labor in the classical system.

#### Labor Demand Curve

The two conditions required for determining the level of demand for profit-maximizing firms are

i.MP_{L} = w/P

ii.P x MP_{L} = w.

The first expression states that labor demand is a derived demand rather than a direct demand which changes according to its productivity. According to this expression, a profit maximizing firm in a perfectly competitive firm will hire labors to a point where **real wage** is equal to **marginal product of labor**. The productivity of labor depends on the production function as it is combined with other inputs of production. Since labor is the only varying factor in this situation, the production function gives the MP_{L}; so, MP_{L} becomes the demand curve for labor, L_{d}.

Mathematically,

L_{d}= g (w/P)

Labor demand has an inverse relation with real wage (w/P) because when the real wage is high, firms demand less labor and they would be willing to employ more labor when the real wage is low. On contrary, labors would be willing to supply more workers when the real wage is high because it is adjusted for the average price level of goods and services and it reflects the true purchasing power of the worker’s income.

Hence, workers supply more labor when the money wage rises relative to the price level. This is illustrated by the diagrams below

#### The Supply of Labor

The supply of labor in the market is determined by the factors such as money wage offered in the market, growth of labor in the economy, labor’s choice for work or leisure, and taxes on income imposed by government.

Classical economists assumed that the supply of labor is mostly influenced by the desire of the workers to work or have more leisure time. This further depends on an individual’s attempt to maximize satisfaction. Since satisfaction can be gained from both real income and leisure time, a trade-off exists between the two, where either consumption for goods and services must be reduced or the labor supply must be reduced.

In order to ease the effect of trade-off*, classical economists justified the supply of labor as a positive function of real wage in terms of disutility of work*. On the basis of this hypothesis, larger real reward can motivate labors to work more than prefer leisure time. Since work involves disutility, workers should be rewarded greater real income to induce them to put in more effort.

Increase in real reward means higher real wage, not just money wage. So, a positive relationship between real wage and supply of labor can be derived from it. Mathematically,

L^{S} = h (w/P)

Graphically, the labor supply curve is upward sloping that shows a positive relationship between real wage rate and quantity of labor supplied.

In the figure, when the real wage increases from (W/P)_{1} to (W/P)_{2, }the quantity supplied for labor also increases from L_{1 }to L_{2}. This states that a positive relationship exists between quantities supplied of labor and real wage.