Economics 0401

Homework Problems #1: Answers

NOTE: * Indicates that a graph is required.

1. Using the material from lecture on Supply and Demand, analyze the following:

*a. Assume there are two markets for labor - a military market and a civilian market - and there is a wage differential between these two markets. Show and explain the difference between a volunteer army and a conscript army.

The basic principle here involves the opportunity cost of labor in its civilian capacity. Assuming that a term of service in the military involves some hardships or other undesirable features, the military will have to pay more to recruits than they receive in civilian employment if it wishes to attract enough recruits. That is, the wage differential compensates recruits for the undesirable features of military life. Notice here that the cost of a volunteer army is borne by all the taxpayers.

What would happen to this differential if a shooting war required the army to increase its troop strength? What would happen if everyone saw military life as more desirable than civilian life?

L₁ - L₃ = L₀ - L₂

The military recruiters ignore the opportunity cost of labor by conscripting workers (anyone between the ages of 18 and 21). This occurs because Congress does not want to pay recruits very much, so at the wage (W_C) mandated by Congress there is an excess demand. The military must then make up this difference between supply and demand by conscription. Conscription will then increase the military supply curve and decrease the civilian supply curve.

Note that (1) civilian wages will be higher in this example than in the volunteer example, (2) a welfare loss from the forcible conscription of teenagers occurs (can you explain why?), and (3) there is an implicit tax burden on recruits who are conscripted as well as those who volunteer. There is one other cost to using the method of conscription: conscripted soldiers are not very productive soldiers (unit cohesion suffers, many more men are needed to do a given number of tasks, etc.), and the military uses labor intensive solutions to problems that might otherwise be mechanized (because labor is artificially cheap). Such conditions would probably make our soldiers less effective in combat (compare Vietnam War to the Gulf War).

NOTE: In the Military Market: (1) represents Conscript Gains from Trade taxed away by lower wages, (2) represents part of the Conscript Supply Price taxed away, and (3) represents Volunteer Gains from Trade taxed away.

*b. How would a decrease in the unemployment rate affect the supply of military recruits? The military wage?

The explanation here involves the idea of opportunity cost once again. Presumably when the unemployment rate is high (especially for teenagers), the possibility of earning a given wage in the volunteer army looks more attractive (relative to the alternative of being unemployed or employed part-time--thus the opportunity cost of taking a job in the military would appear to be lower in times of high unemployment). Thus high unemployment would cause the supply of recruits in the military market to increase. Reversing this reasoning would lead to the implication that a falling unemployment rate would shift the supply curve of recruits to the left and increase the wage because the opportunity cost of foregoing civilian employment has risen, opening up a wider wage differential. NOTE: these supply shifts would be much smaller for the conscription case. Can you explain why?

*c. Graph and explain what might happen when the government puts a ceiling on CEO pay for public corporations which reduces CEO pay below its current level. Assume that there are two labor markets, one for public corporate CEOs and one for private corporate CEOs and that the initial wage differential between the two markets is zero. Explain how a welfare loss and a misallocation of labor resources occurs because of this policy.

When a ceiling on CEO pay is imposed on public corporations this reduces the quantity supplied of CEOs while increasing the quantity demanded thereby creating a shortage of CEOs in the public corporation labor market. CEOs whose supply price (wage) was above the ceiling but below the old equilibrium wage will move to the private corporation CEO labor market and increase the supply there until the equilibrium wage differential between the two labor markets is again zero. A misallocation of labor (a welfare loss) occurs because these CEOs could have generated higher value (and therefore receive higher wages) in the public corporation labor market before the ceiling was imposed but must move to the private corporation labor market where they generate lower value as reflected by the lower wage that they receive. What would you expect to happen to the quality of CEOs hired by public Corporations?

d. EXTRA CREDIT: Show and explain what happens to the wage differential between ice road truckers in Alaska and truckers in the lower 48 states when oil production is expanded in Prudhoe Bay and more truckers are needed in Alaska. Assume the two markets are initially in equilibrium.

2. Using the material from lecture on the demand curve, do the following:

*a. In a recent survey of health economists, 90% of them agreed with the statement “Workers pay for employer-sponsored health insurance in the form of lower wages or reduced benefits.” Show and explain how labor markets for primary and secondary workers will be affected by this and explain why such a program would produce welfare losses. (Hint: Be sure to explain what a welfare loss is.)

Primary workers have very inelastic supplies and when the health mandate (tax) is imposed on employers most of the tax burden will be passed along to primary workers in the form of much lower wages. Employment losses will be minor as will welfare losses (because with relatively few workers being displaced by the tax and moving to lower valued uses the welfare losses or misallocations of labor will be relatively small).

Secondary workers have much more elastic supplies and will simply drop out of the labor force rather than take a wage cut. This implies a relatively small drop in the wage (with employers thereby bearing most of the burden of the tax) but a very large drop in employment (implying very large welfare losses as a very large number of workers are displaced and move to a lower valued use). Employers may seek to screen out any future employees who don’t seem to have a strong attachment to the labor force so that they don’t have to bear such a large burden of the tax.

Question: What happens to the workers who are displaced by the health mandate?

*b. Assuming unskilled labor and capital are gross substitutes and skilled labor and capital are gross complements, show and explain how an investment tax credit will affect these two labor markets. Explain how the skill composition of employment changes.

An investment tax credit of 10% means that an employer making a $1m investment today will be able to reduce his tax payments to the government by $100,000. In effect, a $1m piece of capital equipment only costs $900,000 which is a fall in the price of capital. This change in the price of capital will affect both the skilled and the unskilled labor markets.

In the skilled labor market, a reduction in the price of capital will cause the demand for skilled labor to increase when skilled labor and capital are gross complements-the scale effect dominates the substitution effect. More precisely, a fall in the price of capital will decrease the cost of production and hence increase output (the supply of output increases) which causes the demand for skilled labor to increase. When the relative price of capital falls, more capital is gradually substituted for skilled labor causing the demand for skilled labor to decrease. Since the scale effect dominates the substitution effect demand for skilled labor ultimately increases.

In the unskilled labor market, a reduction in the price of capital will cause the demand for unskilled labor to decrease because unskilled labor and capital are gross substitutes. More precisely, a fall in the price of capital will decrease the cost of production and hence increase output (the supply of output increases) which causes the demand for unskilled labor to increase. When the relative price of capital falls, more capital is gradually substituted for unskilled labor causing the demand for unskilled labor to decrease. Since the substitution effect dominates the scale effect demand for unskilled labor ultimately decreases.

As a result of the increase in demand for skilled labor and decrease in demand for unskilled labor, the wage differential between the two types of labor widens. Since this larger differential is larger than the equilibrium differential, it should induce some unskilled labor to obtain training which raises their skill level (and allows them to work in the skilled labor market). That is, the supply of unskilled labor should gradually decrease and the supply of skilled labor should gradually increase in the long-run until the equilibrium wage differential is reestablished.

In summary, the investment tax credit increases the skill composition of the labor force (supposing that skilled and unskilled labor conform to the assumptions made above).

*c. EXTRA CREDIT: Show and explain how the elimination of the corporate income tax affects labor markets. (Hint: Start with a tax in place in the capital market and show what happens in capital markets when the tax is abolished.) Are capital and labor gross substitutes or gross complements? Explain.

3. Using the material from the lectures on elasticity and the minimum wage, do the following:

*a. Assume two groups of workers A and B where workers in group A are relatively unskilled 16-19 year olds and workers in group B are relatively more skilled 20-24 year olds with more schooling and experience. Also assume that these two markets start with an equilibrium wage differential before the minimum wage is imposed. Then impose the minimum wage in the market for group A (assuming group B’s wages are above the minimum wage). Show and explain what happens in these two markets when group A and B are gross substitutes.

In this case we get a labor-for-labor substitution which partially explains why imposition of the minimum wage seems to have rather minimal impacts on employment. Here’s how it works. With the introduction of the minimum wage for group A, employers of workers in group A will experience increased costs of production which will cause output to fall (because the supply of output decreases). The scale effect causes the firm to decrease its demand for all other inputs including the demand for group B workers. However, the substitution effect works in the opposite direction: the relative wage of group A has increased (relative to Group B’s wage) causing employers to increase their demand for substitutes in group B. With the substitution effect being greater than the scale effect, the overall demand for labor in group B increases, meaning groups A and B are gross substitutes.(Note: W₁ > W_min > W₀ )

*b. When the minimum wage law was first introduced in 1938 the seamless hosiery industry which was one of the largest manufacturing industries in the South was significantly affected by this law. Northern manufacturers who paid their workers higher wages (because their opportunity costs were higher) strongly supported this law in order to hamper competition from their lower cost competitors in the South (where wages were lower). Assume two labor markets for seamless hosiery workers, one in the North (N) and one in the South (S) before passage of the law with a wage differential between them. Then impose the minimum wage law which only affected the Southern labor market. Show and explain what happened to these two markets after the law was passed. (Hint: What happened to the output markets in both the North and South?)

Data indicate that employment in Southern mills fell by 5.5% (employment fell 17% in mills that paid wages below the minimum) while employment in Northern mills expanded by 4.9%. The increased cost of production for Southern mills caused the supply of output to decrease thereby decreasing output and raising the price of hosiery made in the South. This caused the demand for Northern hosiery output to expand, causing demand for hosiery workers to expand as well (remember the demand for labor is a derived demand). This example suggests that support for the minimum wage can arise from those firms which want to cripple their lower-cost rivals.

*c. "Each time the minimum wage has been raised total employment has continued to grow. Therefore, those who claim that the minimum wage causes job loss are simply not correct." Graph and analyze this statement. Is it true or false? Why?

This statement is false. The reason why employment growth occurs arises from economic growth in the economy. This growth means that ouput demands are increasing and causing the demand for labor in most markets (including the covered minimum wage markets) to increase. The job growth occurs because of the increasing demand for labor, not because the minimum wage has been raised. Note that job growth in the minimum wage market will only occur if the rate of growth of demand exceeds the rate of growth in the minimum wage. Why might this be the case?

*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.