Labor Economics Assignment
Task 1: Equilibrium in the Labor Market
First, we examine the equilibrium in the domestic labor market, before any immigration. Below, you are tasked with deriving and describing the domestic labor supply, then the domestic labor demand, and then the equilibrium.
(a) Suppose that in the domestic market, workers derive utility from consuming goods and consuming leisure according to the following utility function: u(X, L) = XßL1-ß where ß=1/2. Let the total time available to each worker T = 100. The government guarantees a minimum income of V = 1600.
(i) Define the reservation wage. Derive it for the worker. Hint: Normalize the price of other goods to 1, and find the MRS.
(ii) Solve for the worker's optimal amount of labor supplied, resulting leisure, and resulting consumption of other goods, when w=10. Graph your solution.
(iii) True/False and Explain: If this worker were more skilled, then his labor supply would be greater.
(b) Let a typical firm's technology be given by Q = 2K1/3L2/3. The firms operate in an output market that is perfectly competitive, with P=24.
(i) Suppose that each firm's capital is fixed at K- = 27. Determine the typical firm's short-run labor demand.
(ii) True/False and Explain: If the production function were instead 4K1/3L2/3, then labor demand would be greater.
(iii) True/False and Explain: If the firm operated instead in an output market in which it has market power, then its labor demand would be greater.
(c) Suppose that there are 10000 workers, and 100 firms. Derive the equilibrium wage and number of hours each worker works. Graph your answer.
Task 2: Immigration and the New Equilibrium
In many developed countries, immigration has been a major issue, as economic migrants or war refugees enter or try to enter the U.K., the U.S., Germany, Australia, and other countries. Each country, and each cohort of migrants, is different, but we can still use the labor-leisure model to understand labor supply and the effects in the domestic labor market.
Suppose that the immigrants are equally skilled to those in the domestic labor market that we are examining. However, unlike the domestic workers, their non-labor income is V = 0.
(a) Do you think that the immigrants have generally lower, similar, or higher reservation wages than domestic workers? Explain. Derive the reservation wage.
(b) Which group, domestic workers or immigrant workers, has more elastic labor supply? Why? Compute: As you deem appropriate, either (i) choose one wage, and then compute the elasticity for each group at that wage; or, (ii) choose two wages and then compute the elasticity for each group between those two wages.
(c) Let there be 5000 immigrants with the same preferences as the domestic workers; however, for them, V = 0. Derive the new market labor supply and the new equilibrium wage. What changes have the domestic workers experienced, both to the number of hours that they work and to the wage that they receive?
Task 3: Welfare Effects of a Quota or a Tax
Consider the three constituencies, the firms, the domestic workers, and the immigrants. Claim 1: Without any market intervention, the firms and immigrants are better off than they would have been but, Claim 2: the domestic workers are worse off, than if the immigrants had remained where they were.
(a) Using economic reasoning, explain Claim 1 and Claim 2.
In an effort to mitigate the losses of the domestic workers, the government considers two policies. You are to evaluate the welfare effects of each policy.
First, show graphically the labor demand, the domestic labor supply, and the immigrant labor supply, labeling both the equilibrium prior to the immigration wave and after it. You may use the labor demand and labor supplies from Tasks 1 and 2, or just graph any reasonable labor demand and labor supplies. Call this the Immigration Graph.
(b) Suppose that the government imposes a quota, allowing only half of the immigrants to enter.
(i) Reproduce the Immigration Graph and now show the effects of the quota: Hint: what happens to the immigrant labor supply? Then, consider what happens to the total labor supply. Show the quota-imposed equilibrium wage and employment level.
(ii) Determine the change, relative both to pre-immigration and to no quota, in the number of hours that the domestic workers work and their wage. Show the change graphically. Explain.
(iii) Determine the change, relative to no quota, in the number of hours that the immigrant workers work and their wage. Show the change graphically. Explain.
(iv) Show graphically the change in the profit of the firms -- what are the two sources of this?
(c) Suppose that the government imposes a tax on the firm for each immigrant that it employs.
(i) Reproduce the Immigration Graph. Determine, graphically, the amount of the per-immigrant tax such that firms would employ the same number of domestic worker-hours as under the quota. Compare the resulting wage for domestic workers with the wage that prevails with the quota.
(ii) Discuss the other welfare effects of the tax versus the quota.
Task 4: Technological Improvement to Production Technology
In the news, find a source of a technological change that affects a firm or industry. You may use any technological change from the recent past or one that is in the near horizon.
Discuss the predicted effects of this change. You should appeal to: (i) the substitution and scale effects; (ii) the value of the marginal product; and (iii) the labor supply. In particular regarding labor supply, will firms demand a different set of skills that their workers need, compared with what their current workers possess?
Will, or might, this require either immigration of skilled workers or worker retraining?
Compensating Wage Differentials
In the news, find a source of a compensating wage differentials in a firm or industry. You may use any compensating wage differential that is current, or from the recent past or one that is in the near horizon. Discuss why the compensating wage differential exists.
Consider a new cohort of workers such that the resulting compensating wage differential will be smaller with the addition of this cohort. Describe how this cohort's preferences differs from the initial cohort. Show graphically.
Words: 1500
3 references.