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You can either take a bus or drive your car to work. A bus pass costs $5 per week, whereasdriving your car to work costs $60 weekly (parking, tolls, gas, etc.). You spend half-an-hour less ona one-way trip in your car than on a bus. How would you prefer to travel to work if your wage rateis $10 per hour? Will you change your preferred mode of transportation if your wage rate rises to$20 per hour? Assume you work five days a week and time spent riding on a bus or driving a cardoes not directly enter your utility.
Taking a bus will save you $55 a week, but it will cost you 5 hours of leisure time due to the longercommute. Since the price of leisure is equal to the wage rate, the monetary value of the time lost is $50when the hourly wage is $10 and $100 when the hourly wage is $20. Therefore, it makes sense for you totake a bus to work if you are paid $10 per hour, but you will switch to driving your car if your wageincreases to $20 per hour.
What happens to employment in a competitive firm that experiences a technology shock suchthat at every level of employment its output is 200 units/hour greater than before?
Because output increases by the same amount at every level of employment, the marginal product oflabor, and hence the value of the marginal product of labor, does not change. Therefore, as the value ofthe marginal product of labor will equal the wage rate at the same level of employment as before, thelevel of employment will not change.
Suppose a firm purchases labor in a competitive labor market and sells its product in acompetitive product market. The firm’s elasticity of demand for labor is −0.4. Suppose the wageincreases by 5 percent. What will happen to the number of workers hired by the firm? What willhappen to the marginal productivity of the last worker hired by the firm?
%ΔE / 5% = -0.4 => %ΔE = -2%
Thus, the firm hires 2 percent fewer workers. Furthermore, because the labor market is competitive, themarginal worker is paid the value of his marginal product. As the product market is also competitive,therefore, we know that the output price does not change so that the marginal productivity of the marginalworker increases by 5 percent.
A firm’s technology requires it to combine 5 person-hours of labor with 3 machine-hours toproduce 1 unit of output. The firm has 15 machines in place and the wage rate rises from $10 perhour to $20 per hour. What is the firm’s short-run elasticity of labor demand?
Unless the firm goes out of business, it will combine 25 persons with the 15 machines it has in placeregardless of the wage rate. Therefore, employment will not change in response to the movement of thewage rate, and the short-run elasticity of labor demand is zero.
In a particular industry, labor supply is ES = 10 + w while labor demand is ED = 40 − 4w, whereE is the level of employment and w is the hourly wage.
(a) What is the equilibrium wage and employment if the labor market is competitive? What is theunemployment rate?
(b) Suppose the government sets a minimum hourly wage of $8. How many workers would losetheir jobs? How many additional workers would want a job at the minimum wage? What is theunemployment rate?
(A)In equilibrium, the quantity of labor supplied equals the quantity of labor demanded, so that ES = ED. Thisimplies 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 workequals the number of persons employers are willing to hire.
(B)If employers must pay a 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 theminimum wage and 2 additional people enter the labor force. Under the minimum wage, theunemployment rate would be 10/18, or 55.6 percent.
Suppose there are 100 workers in the economy in which all workers must choose to work a risky or a safe job. Worker 1’s reservation price for accepting the risky job is $1; worker 2’s reservation price is $2, and so on. Because of technological reasons, there are only 10 risky jobs.
(a) What is the equilibrium wage differential between safe and risky jobs? Which workers will be employed at the risky firm?
(b) Suppose now that an advertising campaign, paid for by the employers who offer risky jobs, stresses the excitement associated with “the thrill of injury,” and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of -$10 (that is, she is willing to pay $10 for the right to work in the risky job); worker 2’s reservation price is -$9, and so on. There are still only 10 risky jobs. What is the new equilibrium wage differential?
- (A) The supply curve to the risky
- job is given by the fact that worker 1 has a reservation price of $1, worker 2
- has a reservation price of $2, and so on. As the figure below illustrates, this
- supply curve (given by S) is upward
- sloping, and has a slope of 1. The demand curve (D) for risky jobs is perfectly inelastic at 10 jobs. Market
- equilibrium is attained where supply equals demand so that 10 workers are
- employed in risky jobs; the market compensating wage differential is $10 since
- this is what it takes to entice the marginal (tenth) worker to accept a job
- offer from a risky firm. Note that the firm employs those workers who least
- mind being exposed to risk.
If tastes towards risk change, the supply curve shifts down to S¢ and the market equilibrium is attained when the compensating wage differential is -$1. This is the compensating differential required to hire the marginal worker (that is, the 10th worker). Note that this compensating differential implies that even though most workers (from worker 12 onwards) dislike risk, the market determines that risky jobs will pay less than safe jobs.
Suppose all workers have the same preferences represented by:
U = √w - 2x
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). Let w0 be the wage paid by the clean job and w1 be the wage paid for doing the dirty job. If the clean job pays $16 per hour, what is the wage in dirty jobs? What is the compensating wage differential?
- clean job = (x=0) w0 = wage for clean job
- dirty job = (x=1) w1 = wage for dirty job
- √w0 - 2(0) = √16
- √16 = √w1 - 2(1)
- √w1 - 2(1) = 36
- 36 - 16 = 20
The dirty job pays $36 per hour, so the compensating wage differential is $20
Consider a competitive economy that has four different jobs that vary by their wage and risk level. The table below describes each of the four jobs.
Job A B C D
Risk 1/5 1/4 1/3 1/2
Wage $3 $12 $23 $25
All workers are equally productive, but
workers vary in their preferences. Consider a worker who values his wage and the risk level according to the following utility function:
u(w,r) = w + 1/r^2
Where does the worker choose to work? Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5 (that is, all jobs become A jobs). What wage would the worker now need to earn in the A job to be equally happy following the regulation?
Calculate the utility level for each job by using the wage and the risk level: U(A) = 28, U(B) = 28, U(C) = 32, and U(D) = 29. Therefore, the worker chooses a type C job and receives 32 units of happiness. If she is forced to work a type A job, the worker needs to receive a wage of $7 in order to maintain her 32 units of happiness as 7 + 25 = 32.
The EPA wants to investigate the value workers place on being able to work in “clean” mines over “dirty” mines. The EPA conducts a study and finds the average wage in clean mines to be $42,250 and the average wage in dirty mines to be $47,250.
(a) According to the EPA, how much does the average worker value working in a clean mine?
(b) Suppose the EPA could mandate that all dirty mines become clean mines and that all workers who were in a dirty mine must therefore accept a $5,000 pay decrease. Are these workers helped by the intervention,
hurt by the intervention, or indifferent to the intervention?
(A) The average value is $47,250 - $42,250 = $5,000.
(B) All except the marginal worker are hurt by the intervention. The workers who sort themselves into the dirty jobs are those workers that do not mind dirt, and therefore do not value working in a clean job at $5,000. (Similarly, if all of the workers in the clean jobs were forced to accept dirty jobs for $5,000 more, all of them except the marginal worker would be hurt as they all value working in a clean job at more than $5,000.)
1. Debbie is about to choose a career path. She has narrowed her options to two alternatives. She can either become a nuclear physicist or a stockbroker. Debbie lives twoperiods. In the first, she gets an education. In the second, she works in the labor market. If Debbie becomes a nuclear physicist, she will spend $12,500 on education in the first period and earn $600,000 in the second period. If she becomes a stockbroker, she will spend $55,000 on education in the first period and then earn $650,000 in the second period.
(a) Suppose Debbie can lend and borrow money at a 5 percent rate of interest between the two periods. Which career will she pursue? What if she can lend and borrowmoney at a 20 percent rate of interest? Will she choose a different option? Why?
(b) Suppose business school raise their tuition by $10,000 for the stockbroker program. What career will Debbie pursue if the interest rate is 5 percent?
- (A) PVphysicist = –$12,500 + $600,000/(1.05) = $558,928.6
- andPVstockbroker = –$55,000 + $650,000/(1.05) = $564,047.6
Therefore, she will become a stockbroker. If the rate of interest is 20 percent, however, the present value calculations become...
- PVphysicist = –$12,500 + $600,000/(1.2) = $487,500
- PVstockbroker = –$55,000 + $650,000/(1.2) = $486,666.7
In this case, Debbie becomes a nuclear physicist.
- (B)PVphysicist = –$12,500 + $600,000/(1.05) = $558,928.6
- andPVstockbroker = –$65,000 + $650,000/(1.05) = $554,047.6
- Debbie will, therefore, become a nuclear physicist
Peter lives for three periods. He is currently considering three alternative education-work options. He can start working immediately, earning $100,000 in period 1, $110,000 in period 2 (as his work experience leads to higher productivity), and $90,000 in period 3 (as his skills become obsolete and physical abilities deteriorate). Alternatively, he can spend $50,000 to attend college in period 1 and then earn $180,000 in periods 2 and 3. Finally, he can receive a doctorate degree in period 2 after completing his college education in period 1. This last option will cost him nothing when he is attending graduate school in the second period as his expenses on tuition and books will be covered by a research assistantship. After receiving his doctorate, he will become a professor in a business school and earn $400,000 in period 3. Peter’s discount rate is 20 percent per period. What education path maximizes Peter’s net present value of his lifetime earnings?
PVHS = 100,000 + 110,000/1.2 + 90,000/1.2^2 = $254,167
PVCOL = -50,000 + 180,000/1.2 + 180,000/1.2^2 = $225,000
PVPHD = -50,000 + 0/1.2 + 400,000/1.2^2 = $227,778
Thus, the best option for Peter is to start working upon completing high school.
Jane has three years of college, Pam has two, and Mary has one. Jane earns $21 per hour, Pam earns $19, and Mary earns $16. The difference in educational attainment is due completely to different discount rates. How much can the available information reveal about each woman’s discount rate?
- r1to2 = $19-$16/$16 = 18.75%
- r2to3 = $21-$19/$19 = 10.53%
Having observed their educational choices, we know that Mary’s discount rate is greater than 18.75%, Pam’s is between 10.53% and 18.75%, and Jane’s is less than 10.53 percent.
2006 U.S. Statistical Abstract shows that, among all 25-34 year-olds, the average annual earnings of a high school graduate with no further education was $26,073 while the average annual earnings of a college graduate with no further education was $43,794 in 2003.
(a) (10 points) Assuming college requires five years, show that the annual return to each year of college education averages 10.9%.
(b) (15 points) It is typically thought that this type of calculation of the returns to schooling is biased, because it doesn’t take into account innate ability (i.e., ability in the workplace not due to college) or innate motivation. If this criticism is true, is the actual return to each year of a college education more than or less than 10.9%?
(A) The annual rate of return, x, solves (1+x)5 • $26,073 = $43,794, which yields x =0.10928.
(B) It is typically argued that people who are innately skilled or motivated pursue more education than those who are less innately skilled or motivated, because the cost (psychic and in terms of the time spent in college) are less for the innately skilled or motivated. If true, then the returns to education are over-estimated by this type of simple calculation. Of course, the typical story might be wrong. The innately skilled or motivated might have to give up a lot in terms of foregone earnings in order to attend college, which they might not need in the first place (e.g.,Bill Gates, NBA players). If so, then the returns to education could be under-estimated.
Suppose Carl’s wage-schooling locus is given by:
Years of schooling Earnings
Derive the marginal rate of return schedule. When will Carl quit school if his discount rate is 4%? What if the discount rate is 12%
- Schooling Earnings MRR
- 6 $10,000
- 7 $12,800 28.0
- 8 $16,000 25.0
- 9 $18,500 15.6
- 10 $20,350 10.0
- 11 $22,000 8.1
- 12 $23,100 5.0
- 13 $23,900 3.5
- 14 $24,000 0.4
Carl will quit school when the marginal rate of return to schooling falls below his discount rate. If his discount rate is 4 percent, therefore, he will quit after 12 years of schooling; if his discount rate is 12%, he will quit after 9 years of schooling.
Suppose there are two types of persons: high-ability and low-ability. A particular diploma costs a high-ability person $8,000 and costs a low-ability person $20,000. Firms wish to use education as a screening device where they intend to pay $25,000 to workers without a diploma and $K to those with a diploma. In what range must K be to make this an effective screening device?
In order for a low-ability worker to not pursue education, it must be that $25,000 ≥ K – $20,000 which requires K ≤ $45,000. Similarly, in order for a high-ability worker to pursue education, it must be that K –$8,000 ≥ $25,000 which requires K ≥ $33,000. Thus, in order to use education as a signaling device, it must be that educated workers are paid between $33,000 and $45,000.
What effect will each of the following proposed changes have on wage inequality?
(A) Indexing the minimum wage to inflation.
(B) Increasing wage subsidies paid to firms that hire low-skill workers.
(C) An increase in border enforcement, reducing the number of illegal aliens entering the country.
(D) Increasing the benefit level paid to welfare recipients.
(A) Indexing the minimum wage to inflation should reduce wage inequality because the minimum wage helps prop up the wages of less skilled workers. Note that an increase in the minimum wage may have negative employment effects, but the proposed policy is not to increase the minimum wage but rather simply to prevent it from falling in real terms.
(B) Wage inequality measures the dispersion of wages in the working population. An increase in welfare benefits would likely induce less-skilled workers out of the labor force, and would reduce measured wage inequality by effectively eliminating the bottom of the wage distribution.
(C) Wage subsidies would increase the demand for less skilled workers, reducing wage inequality.
(D) If illegal aliens tend to be relatively less-skilled, the decrease in supply of illegal aliens would raise the relative wage of less skilled workers. In addition, if the less-skilled illegal aliens complement the skills of skilled natives, the reduction in the number of illegal aliens would decrease the wages of skilled natives.In sum, reducing the number of illegal aliens should reduce wage inequality.
(this multiple choice question has been scrambled)
Suppose the firm’s production function is given by:
where Ew and Eb are the number of whites and blacks employed by the firm respectively. It can be shown that the marginal product of labor is then:
MPE = 5/√Ew+Eb
Suppose the market wage for black workers is $10, the market wage for whites is $20, and the price of each unit of output is $100.
(a) How many workers would a firm hire if it does not discriminate? How much profit does this non-discriminatory firm earn if there are no other costs?
(b) Consider a firm that discriminates against blacks with a discrimination coefficient of .25. How many workers does this firm hire? How much profit does it earn?
(c) Finally, consider a firm that has a discrimination coefficient equal to 1.25. How many workers does this firm hire? How much profit does it earn?
- Wb = 100(5)/√Eb
- 10 = 500/√Eb
- 10 = 500/50 => 10=500/√2500
- The firm will hire 2500 black workers
- 10*√2500 = 10*50 = 500
- 100(500)-10(2500) = 50,000-25,000 = $25,000
- The firm earns a profit of $25,000
- Wb = Wb(1+d)
- Wb = 10(1.25)
- Wb = $12.50
- 12.50 = 100(5) / √Eb
- 12.50 = 500/40 => 12.5 = 500/√1600
- The firm hires 1600 black workers
- 10*√1600 = 10*40 = 400
- 100(400)-10(1600) = 40,000 - 16,000 = $24,000
- The firm earns a profit of $24,000
- Wb = 10(2.25)
- Wb = $22.50
- 20 = 100(5)/√Ew
- 20 = 500/25 => 20 = 500/√625
- The firm hires 625 white workers10*√625 = 10*25 = 250
- 100(250) - 20(625) = 25,000 - 12,500
- = $12,500
- The firm earns a profit of $12,500
Suppose the hourly wage is $10 and the price of each unit of capital is $25.The price of output is constant at $50 per unit. The production function is f(E,K) = E½K½,so that the marginal product of labor is MPE = (½)(K/E) ½ .If the current capital stock is fixed at 1,600 units, how much labor should the firm employ in the short run? How much profit will the firm earn?
as price is fixed at $50, MR = 50. Thus, we have:
MPE*MR = (1/2) * √166/E) * 50 = 1000/√E
by setting VMPE = w and solving for E, we find that the optimal number of workers for thefirm to hire is 10,000 workers. The firm then makes (1600)½(10000)½ = 4,000 units of output andearns a profit of 4,000($50) – 1,600($25) – 10,000 ($10) = $60,000.
Cindy gains utility from consumption goods C and leisure L. The most leisure she can consume in any given week is 168 hours. Her utility function is U(C, L) = C× L. This functional form implies that Cindy’s marginal rate of substitution is C / L. Cindy receives$630 each week from her great-grandmother, regardless of how much Cindy works. What is Cindy’s reservation wage?
The reservation wage is the MRS when not working at all. Thus, wRES = MRS at maximum leisure= C / L = $630 / 168 = $3.75.
Consider 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.
(b) In which direction will the scale effect change the firm’s employment and capital stock?
(c) Can we say conclusively whether the firm will use more or less labor? More or less capital?
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).
- (B)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).
- (C)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.