Economics 450 - Assignment 3
Q1. An industry consists of 100 identical firms. It is impossible to establish additional firms since suitable sites for plants do not exist. The price of the product is $10, set in a competitive world market. Each firm has a production function given by
Q = 30L - 0.1L2,
where Q is output and L is labor.
Male and female workers are equally productive and their labor supply curves are given by
Wm = .025 Lm + 80, Wf = .10 Lf - 20
where the subscripts refer to male and female, and Wm and Wf are the respective weekly wages.
The firms combine to form a single monopsony that can pay different wages to men and women. Find Wm, Wf, Lm, Lf and Q.
Q2. Consider a simple economy in which there are just two occupations, coal mining and auto repair. The mining and auto repair industries are perfectly competitive, and they happen to have identical labor demand curves, given by
w = 400 - L
where w is the daily wage (net of any training costs borne by workers), and L is the number of workers employed in the industry, measured in thousands.
There are 420 workers in the economy, 294 men and 126 women, all equally productive in both jobs. All workers prefer auto repair work to coal mining, but the extent of this preference varies from one worker to another. The distribution of equalizing differences over workers is uniform between 0 and $42. Sex and occupational preferences are independently distributed.
a. Find the equilibrium wage differential and occupational distribution for this economy.
b. Suppose Fred is an "average" worker, who considers the equalizing differential to be $21 a day. Does Fred gain or lose from the diversity of preferences in the economy? That is, would Fred be better or worse off if everyone else in the economy had the same preferences as he does?
c. Suppose that women are excluded from coal mining jobs. How will this affect the equilibrium? What will happen to the average wages of men and women? Who will gain under this restriction, and who will lose?
d. Suppose that employers who have excluded women are found liable for damages. How would you compute the damages?
Q3. An economy consists of two regions, the North and the South. The short-run elasticity of labor demand in each region is -0.5. The within-region labor supply is perfectly inelastic. The labor market is initially in an economy-wide equilibrium, with 600,000 people employed in the North and 400,000 in the South at the wage of $15 per hour. Suddenly, 20,000 people immigrate from abroad and initially settle in the South. They possess the same skills as the native residents and also supply their labor inelastically.
a. What will be the effect of this immigration on wages in each of the regions in the short run (before any migration between the North and the South occurs)?
b. Suppose 1,000 native-born persons per year migrate from the South to the North in response to every dollar differential in the hourly wage between the two regions. What will be the ratio of wages in the two regions after the first year native labor responds to the entry of the immigrants?
c. What will be the effect of this immigration on wages and employment in each of the regions in the long run (after native workers respond by moving across regions to take advantage of whatever wage differentials may exist)? Assume labor demand does not change in either region.