Economics 0401

Homework Problems #2: Answers

NOTE: * Indicates that a graph is required.

1. Using the concepts on human capital developed in lecture, answer the following:

*a. Using the signaling model, do the following: If the government reduces subsidies to college education, how will this affect peoples' decisions to go to college and how will employers respond? Explain.

When subsidies decrease, the costs of going to college increase for both the low productivity worker (A) and the high productivity worker (B). The costs may shift enough so that employers may reduce the level of education (the signal acquired) necessary to distinguish between these two types of workers. This is a distinct advantage to H type workers because they now do not have to spend as much as they did before in order to acquire a signal.

b. Explain the following:

(1) Given the work-family-work life cycle of the 'traditional' woman, it would be rational for women to invest in less education than men.

The work-family-work life cycle for traditional women implies an interrupted career and a shorter period of time in the labor force. With fewer years over which to collect returns on an investment in human capital and the possibility of significant deterioration of skills during the absence from the labor force, women tend to invest less in human capital or to invest in more durable skills which do not depreciate very quickly (but have a lower rate of return).

(2) Suppose Congress passes a law requiring all persons aged 18 to enroll in a program of universal national service for 3 years. How will this affect the returns from investment in higher education? Explain.

This program will lower the returns on human capital because it delays entry into the labor force for three years and reduces the time period over which the returns on human capital investments can be collected. As a result, marginal investors (those for whom the PV of the future earnings stream just exceeds the cost, implying a relatively low rate of return) may decide not to go to college.

(3) Suppose firms require all employees to retire at age 65; now suppose Congress passes a law prohibiting firms from requiring retirement at age 65. Explain how this affects the return from investment in higher education.

This may have an ambiguous effect on the return from investment in higher education. On the one hand, those who are close to retirement will reap windfall gains as they can stay in the labor force longer. But younger workers may find their wage trajectory lowered somewhat so that their wages grow more slowly. Slower wage growth translates into lower rates of return on investment for these younger workers. Workers just entering the labor force who note that some close to retirement are earning very high returns on their investments may mistakenly invest in too much education. But those workers who observe the slower wage growth of the younger portion of the labor force will most assuredly reduce their investment in higher education.

*(4) Suppose that college tuition is reduced to zero and textbooks are provided free of charge. Once equilibrium levels of college attendance are reached, what earnings differential would we expect to see between college grads and high school grads? Show and explain (Hint: You need two supply-demand graphs).

The temptation here might be to argue that the wage differential has been reduced to zero. But this is incorrect. The wage differential will narrow so that it is equal to the opportunity cost of acquiring a college education.

c. Suppose a 30 year old unskilled worker who currently earns $16,000 a year enrolls in a community college (CC) for two years. Tuition and books cost him $2,000 a year. After finishing his courses at the CC, he gets a job paying $20,000 a year. Suppose that this job lasts until this worker retires at age 62. Assuming the interest rate is 5%, is this a good investment? Is this an equilibrium differential? Explain. (Hint: Use the annuity formula in the text or lecture.) What if the interest rate is 10%?

If C = $18,000, B = $4,000, T = 30, and i = 5% = 0.05:

1

1 - ─────────

(1 + r)^T

PV = B ──────────────── = Annuity formula

r

PV = ($4,000)(0.7686/0.05) = $4,000(15.372)

= $61,488 at age 32

PV = $61,488(1/1.05²)

= $61,488(0.907) = $55,769.62 at age 30

PV of C = $18,000(.093/.05) = Annuity formula

= $18,000(1.86) = $33,480 at age 30

Given that PV > C, this is a worthwhile investment at a 5% interest rate. This is not an equilibrium differential because PV > C (equilibrium differentials occurs when PV = C). See Figure 6.

If i = 0.10 then:

PV = $4,000(0.9427/0.1) = $37,708 at age 32

PV = $37,708(0.8264) = $31,161.89 at age 30

PV of C = $18,000(.1736/0.1) = $31,248 at age 30

This yields PV < C, so this is not a worthwhile investment at a 10% interest rate.

2. Using the material on migration developed in lecture, answer the following:

*a. Assume that equilibrium wage differentials have been established between U.S. and Mexican low-wage labor markets. Explain how each one of the following policies will affect these two labor markets and the wage differential:

(1) Employer sanctions (fines) for hiring illegal aliens.

This acts as a tax on employers and will shift the demand for labor curve to the left. This narrows the wage differential so that now PV < C and migration will reverse itself as some return to Mexico as US supply curve decreases and Mexican supply curve increases. Our analysis of the burden of the tax would indicate that part of the final burden of the tax is passed on to workers in the form of lower wages. The portion of the final burden passed on to workers depends on the relative elasticities of demand and supply. Be sure you can explain this idea. The additional cost of migration will increase the equilibrium wage differential (but not by the full amount of the employer fine).

(2) Direct fines for illegal aliens when they are caught.

This policy would place the entire initial cost burden on illegal aliens instead of on employers (this policy might therefore be more popular with employers) and causes PV < C as occurred above. Wage differentials would consequently be much the same as the first part because wages to workers do not rise by the entire amount of the fine (i.e. employers implicitly share in the payment of the fine by paying higher wages). Again the supply and demand elasticities will determine how the tax is shared between employers and workers.

(3) Increased Border Patrol activity.

This policy is similar to the direct fine approach in that it places the cost burden directly on the illegal aliens and causes PV < C as above. Their costs increase here primarily because middlemen guides (coyotes) will emerge and offer (for a price, of course) to guide them safely across the border. Wage differentials and migration patterns will be similar to the previous question.

*b. Assume that equilibrium wage differentials have been established between U.S. and Mexican low-wage labor markets. Explain how a recession in the U.S. will affect this wage differential and the flow of immigrants between these two countries.

A recession will cause a decrease in the demand for labor in the US and a reduction in the wage differential between the US and Mexico. This smaller differential will discourage migration to the US and may encourage some temporary (until business conditions improve) return migration to Mexico. These supply changes will restore the old equilibrium wage differential.

*c. Assume that U.S. and Korea have a disequilibrium wage differential between their labor markets that cannot be eliminated because of limits on immigration. If Korean imports into the U.S. are lower-priced (in relative-price terms) than U.S. goods, show and explain what effect this will have on these two labor markets and the wage differential between them.

The relative price difference implies that the demand for US goods will decrease and the demand for Korean goods will increase. Because of the idea of derived demand, these demand shifts cause the demand for US labor to decrease and the demand for Korean labor to increase. These relative demand shifts in the labor markets will narrow the wage differential between the two countries until the equilibrium differential is reached.

*d. How will an increase in the minimum wage affect immigration into this country? Explain using two low skilled labor markets (assume partial coverage for US market).

Assume that migrants from Mexico will find jobs in the uncovered sector and that all workers displaced from their jobs in the covered sector move to the uncovered sector to work. An increase in the minimum wage will decrease the wage differential between Mexico and the US. Assuming that an equilibrium wage differential prevailed before the increase, the increase in the minimum wage will cause migrants from Mexico already in the US to return to Mexico because the wage differential shrinks as more US workers move into the uncovered sector and push wages down (PV < C). This seems like an odd result. Can anyone think of ways to make a more realistic model.

3. Using the material on labor unions developed in lecture, answer the following:

*a. Using the rent-seeking model show what happens to the rent when unionized industries are declining. (Hint: The demand curve will decrease and become more inelastic.)

Along D curve: Unions raise wages from $300 to $340 with a decline in employment of 20 workers. (TWB = Total Wage Bill = $30,00 at w = $300 but falls to $27,200 at w = $340 so D is elastic.) Rent is equal to ($40)(80) = $3,200.

Along D’ curve: Unions raise wages from $150 to $215 with a decline in employment of 10 workers from competitive level. (TWB is $7,500 at w = $150 but $8,600 at w = $215 so D is inelastic.) Rent is ($65)(40) = $2,600 so Union rents are declining in a declining industry.

*b. Using a two sector model with a union labor market and a non-union labor market, show how unions in the home construction industry fared when they increased their wages a great deal in the 1970s by restricting the supply of union labor. (Hint: Use an inelastic demand for the SR and an elastic curve for the LR.)

In the SR, there was little substitutability between union and non-union labor. But as unions significantly raised their wages and shifted their SR supply curve to the left, union built housing became relatively more expensive than non-union built housing. Demand for non-union built housing increased significantly while demand for union built housing decreased (this is equivalent to the demand for union labor becoming more elastic in the LR). The result was a significant decrease in the share of houses built by union labor in the 1970s.

*c. The West Coast Longshoremen had work rules which required shipping companies to have a crew on board a ship and a crew on the dock when it was loading and unloading. Show how this featherbedding arrangement affected the demand for union labor and the rents that longshoremen unions received.

An increase in demand will increase the rents collected by union members as shown above.

(1) Show what happened when the shipping firms introduced containerization. (Hint: Containerization is a technological change in which capital is a gross substitute for labor–containerization makes loading and unloading ships very easy compared to the labor intensive methods of using union labor.)

Containerization will result in a reduction in the demand for union labor (the substitution effect–-where the reduction in the costs of containerization result in an increase in the relative wage of union labor and the subsequent substitution of capital for labor so that the demand for union labor decreases–-outweighs the scale effect--where the reduction in cost of containerization reduces the production costs of shipping firms so that the supply increases, output increases and the demand for union labor increases).

(2) Why did the unions oppose containerization?

Primarily because it reduced the rents they could collect from the shipping companies.

*d. Using some of the Hicks-Marshall laws, explain why unions (1) oppose repealing import quotas, (2) attempt to organize an entire industry (instead of part of it) and (3) try to limit the substitution of other inputs.

(1) Import quotas are an effective way of reducing the number of substitutes for the union-produced output. This strategy produces a demand curve for union-produced output which is more inelastic. A more inelastic demand for output produces a more inelastic demand for union labor, allowing the union to restrict the number of workers by a relatively small amount while increasing the wage a significant amount.

(2) If only a portion of an industry is organized, the remaining unorganized portion of the industry produces output which is a perfect substitute for the union produced output. By organizing the entire industry, unions eliminate this perfect substitute and make the demand for output (and the demand for labor) somewhat more inelastic.

(3) If the elasticity of supply of other inputs is decreased by policies which limit the ability of employers to substitute one input for union labor (electronic printing presses for union typesetters, union work rules which prevent carpenters from doing minor electrical work, requirements to keep firemen on diesel trains, etc.) then the demand curve for union labor will be more inelastic, allowing the union to raise wages significantly.