In this analysis we are going to assume that firms in the economy are competitive. If this is the case then firms’ profit can be given as:
Profit = P*F(K,L) – WL – RK
Where P=price of goods, W=wage, L=amount of labour per unit of time, R=rent cost, K=capital used per unit of time.
This is because:
Profit = Revenue – Costs
Revenue = Price * Quantity Produced
The amount a firm can produce is, like the national output, given as the production function [Y=F(K,L)].
Therefore Revenue = P*F(K,L)
The costs involved are labour costs and capital costs (we will treat raw material costs as capital, since they are being used to produce something else).
Therefore Cost = (wage*labour + rent*capital)
Hence substituting back in we get the formula for Profit as shown above.
We assume firms are competitive because this means that firms are relatively small within their respected markets and therefore can’t significantly affect the market price. Hence P (the price of the good) is fixed because no one firm can influence the price. This is the case with wages and rent, if a firm offers a higher wage than competitors then it will become uncompetitive. It won’t be able to offer a lower wage because this would result in the firm losing labour to competitors. Simultaneously, if a firm paid higher rent than the market price it would be uncompetitive. It wouldn’t be able to purchase capital for a lower rent than the going market rate.
Thus the profits of a firm are dependent on the amount of labour and capital that a firm utilises since P, W and R are taken as given. So how much labour and capital does a firm employ? Well that depends on the marginal product of labour and capital.
Marginal product of labour (MPL) is the amount of extra output a firm receives by employing one additional unit of labour, keeping the amount of capital fixed. This can be expressed as:
MPL = F(K, L+1) – F(K,L)
This formula states that the MPL equals the amount that the total plus an additional worker produces subtracted by the total amount produced. Don’t forget that diminishing marginal returns (see Micro) is likely to occur.
Now that we understand about the MPL we can work out how much labour a competitive profit maximising firm will employ. A firm will continue to hire workers so long as the MPL is greater than the real wage. The real wage is the wage of labour expressed in units of output as opposed to monetary terms and is given as W/P. Suppose the wage rate at a clothes producing firm is £6 per hour and that the price of the goods (clothes) is £2 per item. The real wage is 3 items of clothing per hour. In this case the clothes firm would continue to hire so long as the marginal product of labour is greater than 3 items of clothing per hour.
Another way of saying this is that P*MPL tells us the marginal revenue the marginal worker brings in for the firm. If marginal revenue exceeds the marginal wage then a firm will hire the worker because he/she makes the firm more money than they cost the firm. Hence a firm will continue to hire as long as P*MPL ≥ W.
We can express this information graphically. The MPL curve slopes downwards because of the law of diminishing marginal returns. Firms will hire QDL which is the point where MPL = real wage. This graph shows the firm’s labour demand curve (i.e. the MPL curve = firm’s labour demand curve.
The firm makes a similar decision when deciding how much capital to employ. Marginal product of capital (MPK) is the amount of extra output a firm receives by employing an additional unit of capital, keeping labour fixed, expressed as: MPK = F(K+1, L) – F(K,L). Capital is also subject to the law of diminishing marginal product.
The amount of capital a firm will rent is determined by the real rental price of capital. The additional revenue a firm makes from utilising an extra unit of capital is P*MPK. The cost is the rent, R. Ergo, the additional profit equals (P*MPK)-R.
Δπ =(P*MPK)-R
The real rental price of capital is equal to R/P. Firms continue to hire until MPK = R/P; that is until the marginal product of capital equals the real wage. Another way of saying this is that firms continue to hire whilst P*MPK≥R.
What determines the value of the marginal products? The answer is the quantity and quality of the factors of production. Quality takes the form of education and training for workers and technological ability for capital. If the labour force is better educated and well trained for the industry in which they are working then they will be able to produce more output and hence the MPL will be higher. In fact the health of the labour force is also important; for example if workers are malnourished then their MPL may be lower if they have less energy to work. For capital the better the technology and the quality of the product then the higher the marginal product, for example, a higher quality piece of machinery may be able to produce more goods in a given time (and hence there will be a higher MPK) than a lower quality piece.
The marginal products are also affected by the quantities of the factors of production. Remember that a firm will continue to employ labour/capital so long as the wage is less than the price multiplied by the marginal product (sometimes P*MPL is called the value of the marginal product). Therefore if there was a shift in the supply of labour, let’s say that there is an increase in the number of workers, then the wage rate/rent will fall (due to the market finding a new equilibrium). This means that a given firm would employ more capital/labour because the wage/rent is lower than previously and they will continue to hire until P*MPL reaches the new wage. So the firm now has greater quantities of labour/capital which means the marginal product of labour/capital will necessarily fall due to the law of diminishing marginal returns. Ergo, it can be concluded that an increase in the supply of labour/capital (more workers/capital available) will result in a lower MPL/MPK and hence a lower share of income going to workers/capital-owners and conversely that a decrease in the supply of labour/capital will result in a higher MPL/MPK with a higher share of income going to workers/capital-owners.
Under the assumption that all firms within the economy are profit maximising and competitive then each factor of product is paid by its marginal product. The total real wages (don’t forget this is W/P) paid to labour are MPL*L and the total real rent (R/P) paid to capital owners is MPK*K. Economic profit is the amount of money left over after rent and wages have been paid.
Economic Profit = Y – (MPL*L + MPK*K)
If there are constant returns to scale then economic profit must be zero because all revenues go to the factors of production. This is called product exhaustion and follows from Euler’s theorem.
We can conclude that total output is distributed to labour and capital owners depending on the marginal productivities of labour and capital. The higher the MPL or MPK then the higher the returns to this group.
If we have just said that economic profit is zero then how can firms make a profit? This is because firms are often capital owners themselves and any profit they make will come from their ownership of capital. Firms may also make profit if they are operating in a market which doesn’t follow our assumptions of profit maximisation and perfect competition.
As always with models there are a number of criticisms. Firstly, it can be extremely difficult to calculate the marginal product of a factor of production because it assumes that all workers can work independently which is obviously not true. It is also very hard to measure output in the services industry for certain sectors such as doctors and teachers. We are making the assumption of perfect competition but in the real world there are few markets which operate under complete perfect competition.
Page last updated on 03/08/15
