Intermediate Macroeconomics Questions, due on April 29, 3:00pm (UTC+8)

See Table 1. The profit-maximizing contract since it maximizes the effort per wage ratio.

b) Briefly explain why paying the lowest wage of $ 16 does not maximize profit.

There are two factors that contribute to profit: higher revenue resulting from the higher effort exerted by a worker and smaller cost from paying a lower wage to the worker.

In this instance, the lowest wage reduces the cost but it also yield the lowest exerted effort. Ultimately, this is the least preferred outcome by a firm since the effort per wage is the lowest.

c) Calculate the equilibrium employment.

Insert the values of the profit-maximizing contract in to the labour demand function:

Solving for yields:

The equilibrium employment is:

d) Calculate the equilibrium unemployment.

The number of workers who would like to be employed at is determined from the supply curve, .

The equilibrium unemployment is the difference between the people willing to work, , at the prevailing wage, , and the employed workers, . That is, .

e) Draw a carefully labeled graph to illustrate the equilibrium outcome.

f) Calculate the probability of finding a high skilled job at the efficiency wage.

The probability of finding high skilled job at the efficiency wage is the ratio between the number of employed workers to the total number of skilled workers willing to accept employment at the prevailing wage, .

g) Calculate the wage for unskilled labour at which unskilled workers will stop acquiring skills, e.g., attending post-secondary education.

First, write down the equation that determines whether an unskilled worker has an incentive to acquire skills.

An unskilled worker will not accept employment if the expected income in the skilled sector equals the income in the unskilled sector.

The unskilled wage is the solution to this equation:

h) Briefly explain why the unskilled workers will stop being enticed by the higher wage for skilled workers at the wage in part g).

As the expected income of a skilled worker equals the income of an unskilled worker, an unskilled worker has no incentive to acquire skills.

Question 2

Consider the labour market for unskilled labour, which is perfectly competitive. Firms use both capital and unskilled labour to produce output, where the capital stock is 50, i.e., is fixed in a given period.

The labour demand curve is given by . There are 40 workers willing to work at any positive wage. During the pandemic, the borders are shut down and no workers are permitted to enter or leave the country. In addition, there is no population growth.

a) Calculate the equilibrium employment and wage.

First, substitute the capital stock into the labour demand function:

Then, use the fact that labour supply curve is vertical,

Equilibrium employment is trivially determined but must be verified that the wage is positive by substituting into the labour demand function.

Since the equilibrium wage is positive, is the equilibrium employment.

b) Briefly explain why there is no involuntary employment.

All workers who would like to be employed at the prevailing wage end up employed.

c) Calculate workers’ income, capitalists’ income and total income.

Workers’ income

Capitalists’ income

Total income = 800 + 1,600 = 2,400

For the remainder of the question, suppose that all profit (capital income) is re-invested into new capital.

d) Calculate the new labour demand curve.

First, substitute the initial capital stock plus the re-invested profit (the capitalists’ income) of 1,600 into into the labour demand function:

e) Calculate the new equilibrium employment and wage.

The equilibrium employment and wage are found in the same manner is part b).

f) Calculate the workers’ income, capitalists’ income and total income.

Workers’ income

Capitalists’ income

Total income = 64,800 + 1,600 = 66,400

g) Briefly describe the impact of re-investing profit on total and average income increase.

Total income increases. Average income also increases since the number of both capitalists and workers remains unchanged.

h) Briefly explain how the income gains from the re-invested profit are redistributed between the capitalists and the workers.

The entire income increases are captured by the workers since area C (capitalists’ income after the profit re-investment) equals areas A (capitalists’ income before the profit re-investment)

2