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)
L1-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
(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 ï¿½ = 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
(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
(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.
(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
(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
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
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
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.