房租协议
CHAPTER 7
7-1. Debbie is about to decide 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 cond, she works in the labor market. If Debbie becomes a marine biologist, she will spend $15,000 on education in the first period and earn $472,000 in the cond period. If she becomes a concert pianist, she will spend $40,000 on education in the first period and then earn $500,000 in the cond period.
(a) Suppo Debbie can lend and borrow money at a 5 percent annual rate. Which career will she pursue? What if she can lend and borrow money at a 15 percent rate of interest? Will she choo a different option? Why?
Debbie will compare the prent value of income for each career choice and choo the career with the largest prent value. If the discount rate is 5 percent,
PV Biologist = – $15,000 + $472,000/(1.05) = $434,523.81
and
PV Pianist = – $40,000 + $500,000/(1.05) = $436,190.48.
Therefore, she will become a pianist. If the rate of interest is 15 percent, however, the prent value calculations become
PV Biologist = – $15,000 + $472,000/(1.15) = $395,434.78
and
PV Pianist = – $40,000 + $500,000/(1.15) = $394,782.61.
In this ca, Debbie becomes a biologist. As the interest rate increas, the worker discounts future earnings more, lowering the returns from investing in education.
(b) Suppo musical conrvatories rai their tuition so that it now costs Debbie $60,000 to become a concert pianist. What career will Debbie pursue if the discount rate is 5 percent?
Debbie will compare the prent value of being a biologist from part (a) with the prent value of becoming a pianist. The relevant prent values are:
PV Biologist = – $15,000 + $472,000/(1.05) = $434,523.81
and
PV Pianist = – $60,000 + $500,000/(1.05) = $416,190.48.
Debbie will, therefore, become a biologist.
7-2. 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 cond period as his expens on tuition and books will be covered by a rearch 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 prent value of his lifetime earnings?
The prent discounted values of Peter’s earnings associated with each of the alternatives are
167,254$2
.1000,902.1000,110000,1002=++
=HS PV , 000,225$2.1000,1802.1000,180000,502
=++−=COL PV , and 778,227$2.1000,4002.10000,502=++
智商最高的狗第一名−=PhD PV .
有故事的图片Thus, the best option for Peter is to start working upon completely high school.
7-3. 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?
The returns to increasing one’s education from one to two years of college and then from two to three years of college are
%75.1816$16$19$21=−=to r and %53.1019
$19$21$32=−=to r .
Having obrved their educational choices, we know that Mary’s discount rate is greater than 18.75 percent, Pam’s is between 10.53 percent and 18.75 percent, and Jane’s is less than 10.53 percent.
天堂电影院影评7-4. Suppo the skills acquired in school depreciate over time, perhaps becau technological
change makes the things learned in school obsolete. What happens to a worker’s optimal amount of schooling if the rate of depreciation increas?
点心打一字If the rate of depreciation is very high, the payoff to educational investments declines. As a result, a worker’s optimal amount of schooling will also fall as the benefits of education erode rapidly.
7-5. Suppo workers differ in their ability, but have the same discount rate. Is it possible for the more able workers to choo less schooling?
This result is possible as long as more able workers have lower marginal-rate-of-discount curves. For example, if an 18-year-old basketball player can earn $3 million per year by entering the NBA after high school whereas he would earn $3.25 million per year by entering the NBA after college, the opportunity cost of college ($3 million per year) may be so great that the player opts to skip college. (A similar story might explain why Bill Gates dropped out of Harvard.)
7-6. Suppo Carl’s wage-schooling locus is given by
Years of Schooling Earnings
6 $10,000
7 $12,800
8 $16,000
9 $18,500
10 $20,350
11 $22,000
12 $23,100
13 $23,900
14 $24,000
(a) Derive the marginal rate of return schedule. When will Carl quit school if his discount rate is 4 percent? What if the discount rate is 12 percent?
The marginal rate of return is given by the percentage increa in earnings if the worker goes to school one additional year.
Schooling Earnings MRR
6 $10,000
28.0
7 $12,800
25.0
8 $16,000
9 $18,500
15.6
心理成长报告
10 $20,350 10.0
11 $22,000 8.1
12 $23,100 5.0
静心的诗句
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 percent, he will quit after 9 years of schooling.
(b) Suppo the government impos an income tax of 20 percent on both labor earnings and interest income. What is the effect of this income tax on Carl’s educational attainment?
This is a tricky problem. If Carl is making his educational decision by comparing the marginal rate of return to schooling to some rate of discount that does not depend on the government’s tax policies, then it turns out that Carl’s optimal schooling level is unchanged. It is easy to verify that if the government
impos a 20 percent tax rate on labor earnings in the cond column of the table above, the marginal rate of return to schooling (column 3) remains unchanged. If, however, Carl’s rate of discount is affected by the government’s tax policies (for example, Carl’s rate of discount might be affected by the rate of interest banks pay), then Carl’s educational decision will be affected. For example, if Carl’s rate of discount falls by 20 percent then the amount of schooling acquired goes up becau the marginal rate of return schedule in column 3 of the table has changed.
7-7. In the typical signaling model, it is assumed that the costs of acquiring an education are higher for low-ability than for high-ability workers. Suppo the government subsidizes low-ability workers for the higher costs they incur in obtaining an education. What happens to the signaling value of education? Can there be a perfectly parating equilibrium in this labor market?
If the government subsidizes schooling so that the cost of schooling is the same for all workers, then the signaling value of schooling is lost. There cannot be a perfectly parating equilibrium becau all workers would have the same incentive to obtain the same amount of schooling.
7-8. Suppo 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 u education as a
screening device where they intend to pay $25,000 to workers without a diploma and $K to tho 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 u education as a signaling device, it must be that educated workers are paid between $33,000 and $45,000.
7-9. It has been argued that the minimum wage prevents workers from investing in on-the-job training and discourages employers from providing specific training to low-income workers. Why would the minimum wage have an adver effect on human capital accumulation for low-income workers?
First, when the minimum wage is high, the marginal return to on-the-job investment falls (assuming one can always find a job), and therefore the lowest skill workers may no longer find it uful to engage in on-the-job training.
Second, a firm that offers general or specific training in the first period pays the worker a wage below his or her marginal product while the investment is taking place and above his or her marginal produ
ct in the post-investment period. If the minimum wage prevents the investment-period wage from falling sufficiently, however, firms may not be able to offer the training.
7-10. Jill is planning the timing of her on-the-job training investments over the life cycle. What happens to Jill’s OJT investments at every age if
(a) the market-determined rental rate to an efficiency unit falls?
The marginal revenue of investing in OJT declines so that Jill will invest less at each age.
(b) Jill’s discount rate increas?
If Jill’s discount rate increas she becomes more “prent oriented”, reducing the future benefits associated with OJT. Thus her OJT investments fall.
(c) the government pass legislation delaying the retirement age until age 70.
The marginal revenue of investing in OJT increas becau the payoff period to the investment is longer. Thus, she undertakes more OJT in this ca.
(d) technological progress is such that much of the OJT acquired at any given age becomes obsolete within the next 10 years.
The marginal revenue to investing in OJT declines and the amount of OJT acquired falls.
7-11. In 2000, there were about 9 million students in four-year college institutions in the United States. Believing that education is the key to the future, a presidential candidate propos that the federal government pay the first $3,000 of college expens each year for everyone attending a four-year college. It is expected that this proposal will encourage 3 million more people to enroll in a four-year college each year, but that the graduation rate will fall from 80 percent to 75 percent. What is the yearly projected cost of the program? What is the average cost of the plan per new student attending a four-year college? What is the average cost of each new four-year college graduate?
Under the old plan, 9 million students attended a four-year college each year, with 80 percent (7.2 million) eventually graduating. Under the new plan, 12 million students will attend a four-year college each year, with 75 percent (9 million) eventually graduating. The annual cost of the program, therefore, is 12 million × $3,000 = $36 billion. The average cost of the plan per new college student is $36b / 3m = $12,000. The average cost of each new graduate is $36b / 1.8m = $20,000.
9大行星
