ECON LABOUR ECONOMICS FALL 2007 Queen s University

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1 ECON LABOUR ECONOMICS FALL 2007 Queen s University HOMEWORK ASSIGNMENT #1 Due by the start of class on October 15 PART I Multiple Choice (22 questions, 2.5 points each, 55 points total) (For questions based on Borjas, the chapter and problem number are indicated in parentheses.) 1. An individual with 100 hours a week to allocate between work and leisure has the utility function represented by U(C, L) = 2C 1/2 L 1/2. Suppose this person currently has a weekly consumption of $800 and chooses to work 20 hours per week. What is this person s non-labour income per week (V) and hourly wage (w)? A. V = $0 and w = $15 B. V = $600 and w = $8 C. V = $200 and w = $10 D. V = $280 and w = $8 E. V = $600 and w = $ (2-11) Among single, college-educated women aged 22 25, average annual hours worked is 2,100 and the average wage is $21. If the average wage increases to $25 per hour, average annual hours worked increases to 2,300. What is the elasticity of labour supply for this group of workers? A B. 0.5 C. 1.4 D. -1 E After a decrease in the wage, a firm s LR optimal use of capital and labour changes so that A. the amount demanded of capital decreases, while the amount demanded of labour can decrease or increase B. the amount demanded of labour increases, while the amount demanded of capital can decrease or increase C. the amount demanded of labour increases, while the amount demanded of capital decreases D. the amount demanded of both inputs decreases E. the amount demanded of both inputs increases 4. Which of the following is true for the "backward-bending" range of the labour supply curve? A. The income effect is dominated by the substitution effect. B. The substitution effect is dominated by the income effect. C. There is no income effect. D. There is no substitution effect. E. The income and the substitution effects exactly offset each other. 1

2 5. The theory of compensating differentials predicts that A. holding worker characteristics constant, workers in safer jobs will earn less B. workers in risky jobs will always earn more than those in safe jobs C. holding wages constant, higher skilled workers will have riskier jobs D. firms will always prefer to compensate the workers for the risk of injury rather than making their jobs safer E. both B) and C) are true 6. The following diagram illustrates the budget line for a worker both with (thick line) and without (thin line) a wage subsidy program. The worker has 100 possible hours per week in which to earn $8 per hour. Assume leisure is a normal good. Consumption $800 $600 $ Leisure Consider an individual who would choose to work 30 hours without the program. With the program, the individual will A. definitely work more B. definitely work less C. work the same number of hours because the substitution effect and the income effect always offset each other D. work more if the substitution effect is greater than the income effect E. work less if the substitution effect is greater than the income effect 7. Marla has 100 hours per week to allocate between work and leisure. She has zero non-labour income and faces a market wage of $10/hour. Suppose the government offers Marla a welfare program with an income guarantee of $240 a week, and a negative income tax of t = 0.4. Marla s break-even income is A. Y b = $200 B. Y b = $400 C. Y b = $600 D. Y b = $800 E. Y b = $1,000 2

3 8. If a labour market outcome is not Pareto efficient then A. firms could produce their respective outputs at lower costs. B. all gains from trade have not been exhausted. C. firms are not maximizing profits. D. it is impossible for firms to hire more workers without government intervention. E. nobody can be made better off without making at least one other person worse off. (4-1) Questions 9 and 10 refer to the following problem: Suppose there are two inputs in production, labour (E) and capital (K), where K measures the number of machines. The existing technology is described by the production function q = 2E + 3K and the price of capital is $835 per machine per week. The firm wants to produce 90 units of output. 9. What combination of inputs will the firm use if the weekly salary of each worker is $400? A. E=0, K=30 B. E=0, K=90 C. E=90, K=0 D. E=45, K=0 E. E=30, K= What is the elasticity of labour demand (in absolute value) as the wage increases from $400 to $600? A. 0 B. infinite C D. 3 E. 1/3 11. (4-2b) What happens to the long-run demand curve for labour if the price of capital decreases? A. The demand curve for labour shifts up. B. The demand curve for labour shifts down. C. The demand curve does not shift, but the firm moves to a different point along the same demand curve. D. The demand curve for labour shifts up if the substitution effect is stronger and shifts down if the scale effect is stronger. E. The demand curve for labour shifts down if the substitution effect is stronger and shifts up if the scale effect is stronger. 12. Consider an economy with two sectors, A and B. In the absence of government regulation, the equilibrium wage in each of the two sectors would be $320 per week. However, sector A is covered by a minimum wage of $400 per week, while sector B is not covered by a minimum wage law. Workers can seek jobs in either of the two sectors, but a worker who seeks a job in sector A and does not find one remains unemployed and receives an unemployment benefit of u 0 = $100 per week. The probability a worker can find a job in sector A is 0.8 (i.e., 80 percent). The utility of an employed worker is U = w, where w is the worker s wage; the utility of an unemployed worker is u 0. In equilibrium, what will be the weekly wages paid by the firms in the two sectors? A. w A = $420 and w B = $320 B. w A = $420 and w B = $100 C. w A = $400 and w B = $360 D. w A = $400 and w B = $340 E. w A = $400 and w B = $400 3

4 13. (4-7) Suppose a firm purchases labour in a competitive labour market and sells its product in a competitive product market. The firm s elasticity of demand for labour is Suppose the wage increases by 2.5%. What will happen to the number of workers hired by the firm and to the marginal productivity of the last worker hired by the firm? A. The firm hires 1% more workers; the marginal productivity of the marginal worker increases by 5%. B. The firm hires 2.5% fewer workers; the marginal productivity of the marginal worker increases by 1%. C. The firm hires 1% fewer workers; the marginal productivity of the marginal worker increases by 2.5%. D. The firm hires 5% more workers; the marginal productivity of the marginal worker decreases by 2.5%. E. The firm hires 2.5% more workers; the marginal productivity of the marginal worker decreases by 1%. 14. (6-4) Suppose all workers have the same preferences represented by U = w x where w is the wage and x is the proportion of the firm s air that is composed of toxic pollutants. There are only two types of jobs in the economy, a clean job (x = 0) and a dirty job (x = 1). If the clean job pays $9 per hour, the compensating wage differential is A. $9 B. $20 C. $16 D. $7 E. $4 15. (7-6) Suppose Carl s wage-schooling locus is given as follows: Years of Schooling Earnings 6 $10,000 7 $12,800 8 $16,000 9 $18, $20, $22, $23, $23, $24,000 If his discount rate is 6 percent, Carl will quit school after A. 12 years of schooling B. 10 years of schooling C. 9 years of schooling D. 11 years of schooling E. 13 years of schooling 16. (6-9) There are two types of farming tractors on the market, the FT250 and the FT500. The only difference between the two is that the FT250 is more prone to accidents than the FT500. Over their lifetime, one in one-thousand FT250s is expected to result in a fatal accident, as compared to only one in four-thousand FT500s. The FT250 sells for $125,000 while the FT500 sells for $140,000. At these prices, 2,000 of each model are purchased each year. The statistical value of a life of a farmer is A. $10 million B. $15 million C. $5 million D. $12 million E. $8 million 4

5 17. (7-8) Suppose there are two types of persons: high-ability and low-ability. A particular diploma costs a high-ability person $10,000 and costs a low-ability person $30,000. Firms wish to use education as a screening device where they intend to pay $530,000 (in lifetime earnings) to workers without a diploma and $K to those with a diploma. Education will be an effective screening device if A. K = $535,000 B. K = $545,000 C. K = $565,000 D. K = $570,000 E. K = $575, Workers choose whether to work in a risky or in a safe job. Suppose there are 100 workers in the economy. Worker 1 s reservation price (for accepting the risky job over an equivalent safe job) is $1; worker 2 s reservation price is $2, and so on. Because of technological reasons, there are only 12 risky jobs and they all need to be filled. What is the equilibrium compensating wage differential between safe and risky jobs? A. $12 B. $6 C. $1 D. $100 E. $ If a firm has monopsony power, then A. the firm s workers are paid more than the value of the marginal product of their labour. B. the firm s workers are paid exactly the value of the marginal product of their labour. C. the price of the firm s product is less than the value of the marginal product of the workers labour. D. the price of the firm s product is more than the value of the marginal product of the workers labour. E. the firm s workers are paid less than the value of the marginal product of their labour. 20. Consider a firm with production function q = 200EK, where q is output and E and K are amounts of labour and capital, respectively. If the wage rate is w = $12 per hour and the price of capital is r = $6 per hour, what is the cost minimizing combination of E and K required to produce q = 1,600 per hour? A. E=2 and K=4 B. E=6 and K=12 C. E=120 and K=60 D. E=8 and K=1 E. E=1 and K=8 21. Suppose average product of labour is increasing with employment. At this employment level, A. the marginal product is less than the average product. B. the marginal product is greater than the average product. C. the marginal product is equal to the average product. D. the marginal product can be either less than or greater than the average product. E. the average product is maximized 22. Suppose the labour supply of men is estimated as w = E M and the estimates for the labour supply of women yield w = E W, where w is the market wage. Based on these estimates, the aggregate supply of labour is given by A. w = ( E S )/7 B. w = E S C. w = E M + 20E W D. w = E S E. w = ( E S )/11 5

6 PART II Short questions (6 questions; 45 points total) Write your answers in the assignment, always on the page on which the question is given. Always provide an explanation for your final answer, or indicate how you got it. Label clearly any line you draw. Try to be brief; points are subtracted for extraneous material. 1. (2-4) 5 pts. Tom earns $20 per hour for up to 40 hours of work each week. He is paid $40 per hour for every hour in excess of 40. Tom faces a 30 percent tax rate and pays $4 per hour in child care expenses for each hour he works. Tom receives $100 in child support payments each week. There are 100 hours in the week to allocate between work and leisure. Graph Tom s weekly budget line. 6

7 2. (2-8) 9 pts. Shelly s preferences for consumption and leisure can be expressed as U(C,L) = ( C 220 )( L 10 ). There are 100 hours in the week available to split between work and leisure. Shelly earns $8 per hour after taxes. She also receives $300 worth of welfare benefits each week regardless of how much she works. (a) 2 pts. Graph Shelly s budget line. (b) 3 pts. What is Shelly s marginal rate of substitution when L = 40 and she is on her budget line? (c) 4 pts. Find Shelly s optimal amount of consumption and leisure. 7

8 3. (4-9) 8 pts. In a particular industry, labour supply is E S = w while labour demand is E D = w, where E is the level of employment in 1,000s of workers and w is the hourly wage. (a) 4 pts. What is the equilibrium wage and employment if the labour market is competitive? What is the unemployment rate? (b) 4 pts. Suppose the government sets a minimum hourly wage of $12. How many workers would lose their jobs? How many additional workers would want a job at the minimum wage? What is the unemployment rate? 8

9 4. (4-10) 7 pts. Suppose the wage is $30 per hour and the price of each unit of capital is $25 per hour. The price of output is constant at $50 per unit. The production function is f(e,k) = 2E ½ K ½, where E represents the number of labour hours. If the current capital level is fixed at 900 units, how much labour should the firm employ in the short run? How much profit will the firm earn? 5. (5-7) 7 pts. An economy with short-run elasticity of labour demand of 0.25 has perfectly inelastic labour supply. The labour market is initially in an economy-wide equilibrium, with 400,000 people employed at the wage of $15 per hour. Suddenly, 20,000 people immigrate from abroad. They possess the same skills as the native residents and also supply their labour inelastically. Calculate the effect of this immigration on wages in this economy. 9

10 6. (7-1) 9 pts. Debbie is deciding which career path to pursue. She has narrowed her options to two alternatives. She can either become a marine biologist or a concert pianist. Debbie lives two periods. In the first, she gets an education; in the second, she works in the labour market. If Debbie becomes a marine biologist, she will spend $25,000 on education in the first period and earn $500,000 in the second period. If she becomes a concert pianist, she will spend $33,000 on education in the first period and then earn $510,000 in the second period. In making her choice, Debbie only cares about the present value of her lifetime earnings. (a) 5 pts. Suppose Debbie can lend and borrow money at a 5% annual rate. Which career will she pursue? (b) 4 pts. What if Debbie can lend and borrow money at a 10% rate of interest? Will she choose a different option? Why? 10