ECON153 LABOR MARKET

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ECON 153: 2nd July 2020 (Thursday)

Total Points (40)

Problem Set #1

1. Suppose that the wage distribution for Riverside is given below:

Sector Number of Workers Wage

A 40 $10 (per hour)

B 30 $5

C 30 $5

a. Compute the level of wage inequality for the town using the 90th / 10th percentile ratio and the 90th / 50th and 50th /10th ratios. (3 points)

b. Assume a minimum wage law is passed that doesn’t affect the market in the high- wage sector A but boosts wages to $7/hour in sector B, the covered sector, while

reducing employment to 20 in that sector. Displaced workers in sector B move into

the uncovered sector, C, where wages fall to $4.50 per hour as employment grows

to 40. Has wage inequality risen or fallen? Does your answer change depending

on the measure of wage inequality you use? (2 points)

2. The human resource manager of the Culinary Chameleon makes the following claim: “Our workers make an average of $400 per week. We produce $4500 worth of output

each week using only 10 workers. That averages out to $450 per worker per week. We

should therefore hire more people as long as the wage is $400 per week.” Assess this

claim - is the reasoning solid or do you disagree? (2 points)

3. At Taco Bell, Burritos cost $2.50 (p=2.5) and the market wage for labor is $12.50.

a. Calculate the marginal product of labor (MPL), average product of labor (APL), value of the marginal product of labor (VMPL), and value of the average product of

labor (VAPL) in the chart below. (2 points)

Number of

workers

Burritos MPL APL VMPL VAPL

0 0

1 15

2 28

3 38

4 47

5 54

6 59

2

7 62

8 64

9 65

b. What’s the optimal amount of labor to use (1 point)?

c. What would be the per-hour profits at Taco Bell if capital costs $50 per hour? (1 point).

4. Consider a firm that uses two inputs: skilled workers and computers. Explain what it

means if skilled workers and computers are complements in production. Specifically, if

the price of computers falls, and skilled workers and computers are complements, will the

firm want to hire more or fewer skilled workers? (2 points)

5. Consider a firm that uses both labor and capital in production. The price of capital is $20

per unit and the wage rate is $10 per hour.

a. Draw the firm’s iso-cost line assuming a total production cost of $100. How steep is this line (that is, what is its slope)? Be sure to clearly label the axes. (2 points)

b. Suppose the wage increases to $15 per unit. In which direction does the substitution effect change the firm’s demand for labor and capital? In which direction does the

scale effect change the firm’s demand for labor and capital? (2 points)

c. If the firm chooses its labor and capital combination to minimize its production costs, will the marginal product of labor be higher than, lower than, or equal to the

marginal product of capital? Why? (Assume that the price of labor and capital are

those given in part b.) (2 points)

6. Suppose the hourly wage is $40, the price of each unit of capital is $50, and the price

of output is $100 per unit. Assume that the firm cannot affect any of these prices. The

production function of the firm is

𝑓(𝐿, 𝐾) = √𝐿𝐾

a. Find MPL. (1 point)

b. If the current capital stock is fixed at 1,600 units, how many hours of labor should the firm hire in the short run (i.e., what should L be)? (1 point)

c. Set up the profit function. How much profit will the firm earn? (1 point)

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d. Now suppose that the price of labor increases to $50/hour. Find the new optimal level of employment. We remain in the short term, so the level of capital remains

fixed. (1 point)

e. What is the short run elasticity of labor demand? Is labor demand elastic or inelastic? (1 point)

7. Dr. Addink creates micro-chips according to the following production function: Q= f

(L, K) =10√𝐿. The wage of a programmer such as Betty is $100 per hour and the price of each micro-chip is $2000. His capital costs $10000 per hour total.

a. Find the profit function. (1 point)

b. How many hours will Dr. Addink employ Betty, if he is maximizing profits. Hint: MPL=10×1/2× L ^ (-1/2) = 5/L^(1/2) (2 points)

c. Now consider the long run in which Dr. Addink can choose how much capital to employ according to the production function: Q(L, K) = (K^1/4)L^1/2. The price

of capital is $10 per unit per hour. Find the optimal mix of capital and labor to use

in the long run. Use the wage from part a. (2 points)

d. Find the optimal amount of labor and capital in the long run using the optimal mix of capital and labor from part c. (Hint: Write out the new profit function with the

new production function and the cost of capital now being 10 x K.) (2 points)

8. Discuss (or show graphically) why a minimum wage (set above the market wage) produces unemployment in a perfectly competitive model. (1 points)

9. Yogurtland’s frozen yogurt is incredible. It sells delicious yogurts in Riverside. The attached

spread sheet shows their hours/day in labor and their total revenue. Andrew (the owner) hires

people to scoop his frozen yogurt at $12/hour. Use the excel data file FroYoData to answer this

question.

a. Based on this data, what do you believe is the optimal number of workers to hire (round

to the nearest whole number)? (2 points)

b. Why do you think that is the optimal amount of labor to use (attach any graphs, math,

or screenshots of what you used to solve this question)? (2 points)

c. What is the marginal revenue product of labor for the 84th worker-hour (round to the

nearest whole number)? (2 points)

d. What might be the problem with inferring that the 92nd worker-hour increased revenue

by approximately $10 using only this data? (2 points)