Exercise Lesson Labor - PowerPoint Presentation

1. Exercise LessonLabor Economics (CLEF)Tutor : Dott.ssa Vitali Beatricebeatrice.vitali8@unibo.itLabor Demand

2. PROBLEM 1Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2.

3. a) In which direction will the substitution effect change the firm’s employment and capital stock?Prior to the price shift, the absolute value of the slope of the isocost line (w/r) was 1.5. After the price shift, the slope is 2. In other words, labor has become relatively more expensive than capital. As a result, there will be a substitution away from labor and towards capital (the substitution effect).

4. Because both prices fall, the marginal cost of production falls, and the firm will want to expand.The scale effect, therefore, increases the demand for both labor and capital (as both are normal inputs).b) In which direction will the scale effect change the firm’s employment and capital stock?

5. c) Can we say conclusively whether the firm will use more or less labor? More or less capital? The firm will certainly use more capital as the substitution and scale effects reinforce each other in the direction of using more capital. The change in labor hired, however, will depend on whether the substitution or the scale effect for labor dominates.

6. PROBLEM 2Suppose a firm purchases labor in a competitive labor market and sells its product in a competitive product market. The firm’s elasticity of demand for labor is - 0.4. Suppose the wage increases by 5 percent. What will happen to the amount of labor hired by the firm? What will happen to the marginal productivity of the last worker hired by the firm?

7. Given the estimates of the elasticity of labor demand and the change in the wage, we have that Thus, the firm hires 2 percent fewer workers. Furthermore, because fewer workers are hired, under normal conditions the marginal productivity of the last worker hired will increase. (More formally, because the labor market is competitive, the marginal worker is paid the value of his marginal product. As the product market is competitive, we also know that the output price does not change so that the marginal productivity of the marginal worker increases by 5 percent.)

8. PROBLEM 3In a particular industry, labor supply is ES = 10 + w and labor demand is ED = 40 - 4w, where E is the level of employment and w is the hourly wage.

9. a) What is the equilibrium wage and employment if the labor market is competitive? What is the unemployment rate?In equilibrium, the quantity of labor supplied equals the quantity of labor demanded, so that ES = ED. This implies that 10 + w = 40 – 4w. The wage rate that equates supply and demand is $6. When the wage is $6, 16 persons are employed. There is no unemployment because the number of persons looking for work equals the number of persons employers are willing to hire at the going wage rate of $6 per hour.

10. b) Suppose the government sets a minimum hourly wage of $8. How many workers would lose their jobs? How many additional workers would want a job at the minimum wage? What is the unemployment rate?If employers must pay an hourly wage of $8, employers would only want to hire ED = 40 – 4(8) = 8 workers, while ES = 10 + 8 = 18 persons would like to work. Thus, 8 workers lose their job following the minimum wage as 16 workers used to be employed but now only 8 are; and 2 additional people enter the labor force following the minimum wage as 16 workers used to want a job but now 18 do. Under the minimum wage, the unemployment rate would be 10/18, or 55.6 percent.

11. PROBLEM 4An economy consists of two regions, the North and the South. The short-run elasticity of labor demand in each region is –0.5. Labor supply is perfectly inelastic within both regions. 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 a 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.

12. There will be no immediate effect on the North’s labor supply in the short run, so the wage rate will not change there. In the South, labor supply will increase by 5 percent as 20,000 is 5% of 400,000. As labor is supplied perfectly inelastically, the wage rate must fall by 10 percent as the elasticity of labor demand is -0.5 (so a one percent decrease in wages would have been generated by a 0.5 percent expansion of the labor supply; as the expansion was 5%, wages must have decreased by 10%). The new hourly wage in the South, therefore, is $13.50 and total employment in the South is 420,000.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)?

13. 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?After the initial migration, we have seen that wages in the South are $13.50 while wages in the North are $15. This difference leads 1,500 natives migrating from the South to the North in the first year. Employment in the North after one year, therefore, is 601,500. Moreover, as the elasticity of labor demand in the North is -0.5 and employment has increased by 0.25 percent, the Northern wage falls by 0.5 percent to roughly $14.93. Likewise, employment in the South after one year is 418,500. As the elasticity of labor demand is -0.5 and employment has decreased by 0.3571 percent, the Southern wage increases by 0.71428 percent to roughly $13.60. Thus, the ratio of the Northern to Southern wage after one year is 1.09779.

14. PROBLEM 5Let total market demand for labor be represented by ED = 1,000 – 50w where ED is total employment and w is the hourly wage.

15. Set ED = ES and solve for w yields w* = $12. At this wage, ED = 400 and ES = 400, which is the equilibrium level of employment.Lastly, producer surplus is the area below the demand curve but above the wage. Mathematically, producer surplus = (0.5) × ($20 – $12) × 400 = $1,600 where the $20 comes from solving for w when ED = 0.a) What is the market clearing wage when total labor supply is represented by ES = 100w – 800? How many workers are employed? How much producer surplus is received at the equilibrium wage?

16. At a minimum wage of $16, labor demand will equal 200 (while labor supply will equal 800). As firms are not required to hire workers if they don’t want to, the new level of employment will be 200 workers. In this case, producer surplus = (0.5) × ($20 – $16) × 200 = $400.b) Suppose the government imposes a minimum wage of $16. What is the new level of employment? How much producer surplus is received under the minimum wage?

17. PROBLEM 6Let total market demand for labor be represented by ED = 1,200 – 30w where ED is total employment and w is the hourly wage. Suppose 750 workers supply their labor to the market perfectly inelastically. How many workers will be employed? What will be the market clearing wage? How much producer surplus is received?

18. As the 750 workers supply their labor perfectly inelastically, all 750 will be employed. The wage that the firms must pay satisfies 750 = 1,200 – 30w which solves as w* = $15. In this case, producer surplus = (0.5) × ($40 – $15) × 750 = $9,375 where the $40 comes from solving for w when ED = 0.