Sample Midterm Exam Solutions. Economics 371 University of Victoria - Spring 2017

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1 Sample Midterm Exam Solutions Economics 371 University of Victoria - Spring 2017 Prof. H.J. Schuetze The midterm exam consists of two agree/disagree questions and two short-answer style questions. There will be a total of 60 marks for the exam. Each of the agree/disagree questions is worth 10 marks. Short-answer questions account for the remaining 40 marks. Be sure to answer each of the questions in full, carefully labelling all graphs that may be used in answering. -- You will be given 80 minutes -- Good Luck!! 1

2 PART I: AGREE/DISAGREE State whether you agree or disagree with each of the following statements. If you agree with the statement, explain why you agree, and if you disagree, explain why you disagree (include the correct statement in your answer). I encourage you to illustrate your answers using diagrams where appropriate. Each question is worth 10 marks. 1. Economic theory suggests that competition will ensure an equal present value of net advantage at the margin. However, in the short-run differentials across markets can arise as the labour market adjusts to the long-run outcome. Agree. Net advantage includes both monetary and non-monetary components associated with working on that particular job. If the above equality did not hold then, at least in the long run, competition would ensure that workers at the margin of decision would move from jobs of low net advantage to those offering high net advantage. Skilled Labour Market Unskilled Labour Market Ss Ss ws Su ws wu Ds Ds Du Ns Nu Despite this, differences in net advantage across occupations can exist in the short run. For example, suppose there exist markets for skilled and unskilled workers whose wages are different, reflecting compensating differentials (ws vs. wu). Now suppose there is a technology change that increases the demand for skilled workers (Ds to Ds ). This shift in demand will increase skilled labour wages to ws since the short-term supply will be fairly inelastic owing to high training costs. Despite this increase in ws, the non-monetary characteristics of skilled and unskilled work will remain the same in addition to unskilled wages. This will increase the net advantage present in skilled occupations relative to unskilled work. In the long run the supply of skilled workers will increase to Ss as individuals move toward the higher net advantage. This adjustment of supply will lower wages back to their previous level. In the long run, skilled and unskilled wages need not be equal given other compensating factors, however, net advantage will be. 2

3 2. Safety regulations that require firms to meet a certain safety standard can make workers better off if the workers have imperfect information on the risks they face. Agree: Suppose that workers perceive they are getting Sp worth of safety along with the observed wage Wa. However, the actual amount of safety provided by the firm is given by the firm s zero profit iso-profit frontier and equals Sa (which is less than Sp). In this scenario, actual utility is given by Ua. Any safety regulation that sets the required level of safety greater than Sa and less than Sr will make workers better off in terms of actual utility. Indeed, the optimal level of the safety standard is given by So, where the isoprofit and indifference curve are tangent. 3

4 PART II: SHORT-ANSWER QUESTIONS 1. [25 marks] Suppose that there are two types of workers in the labour market, low productivity workers and high productivity workers, and that the present value of lifetime productivity is $400,000 and $550,000 for low and high, respectively. In addition, assume that the real costs of a year s worth of university credits is higher for low productivity workers ($50,000) compared to high productivity workers ($30,000) because of the psychic costs. a) [4 marks] Suppose that 40 percent of the population is high productivity. What is the equilibrium wage rate for the high and low productivity workers in the absence of education (i.e. assuming that no such signal exists)? Workers will be paid the average productivity of the group: 0.6 $400, $550,000 = $240,000 + $220,000 =$460,000 b) [8 marks] Now assume that university education is available as described. Assume that firms form beliefs such that if a worker has at least y* years of university, the firm assumes the worker is a high productivity worker and pays lifetime salary of $550,000 and if a worker has fewer than y* years of university the firm assumes the worker is a low productivity worker and pays a lifetime salary of $400,000. For what values of y* will these beliefs result in a separating equilibrium? A separating equilibrium requires that low-productivity workers do not go to university at all. This will occur whenever the net return from getting zero years of university exceeds the net return from y* years. i.e. when $400,000>$550,000-($50,000y*) solving we get y*>3 A separating equilibrium also requires that high productivity workers do get y* years of university. This occurs whenever: $400,000<$550,000-($30,000y*) solving yields y*<5 Putting the two conditions together we get 3<y*<5 4

5 c) [5 marks] In your answer to part (b) there are several values of y* for which an equilibrium will exist. In terms of efficiency, does it matter which of the possible equilibrium belief values for y* the firms settle on? Explain. As shown in part (b) there are an infinite number of equilibrium values for y*. Indeed, it does matter which of the equilibrium values the firms settle on. This is because the equilibria are not equivalent in terms of welfare. In particular, increases in y* hurt the high productivity workers while low productivity workers are unaffected. We get the same separating equilibrium if y* is epsilon lower than 5 as when y* is epsilon greater than 3. The closer to 5 y* is, however, the greater the costs to the high ability workers to achieve the signal (and the greater the inefficiency). d) [8 marks] Assume that firms choose the most efficient value of Y*. Suppose that policy-makers observe the positive relationship between education and wages and assume that education is productive as in the human capital model of education. Thus, they create a program that subsidizes the direct costs (tuition and books) of education for all workers. If the subsidy is $10,000 per student, show that the pay scheme adopted by firms in the economy will not yield an equilibrium. The most efficient value of Y* will be the where Y* is just higher than 3. As in part (b), the separating equilibrium requires that low-productivity workers do not go to university at all. This will occur whenever the net return from getting zero years of university exceeds the net return from y* years where the cost is now $40,000 per year. i.e. when $400,000>$550,000-($40,000y*) solving we get y*>3.75 A separating equilibrium also requires that high productivity workers do get y* years of university. Now the cost to high ability workers is just $20,000 per year. This occurs whenever: $400,000<$550,000-($20,000y*) solving yields y*<7.5 Putting the two conditions together we get 3.75<y*<7.5 The pay scheme adopted by firms will no longer yield a separating equilibrium. All workers are now willing to attend university for 3 plus epsilon years. 5

6 2. [15 marks] Suppose that, on average, an applicant waits 12 months before being hired into a government job (as a mail clerk). George could work as a mail clerk in the private sector immediately for a salary of $2500 per month, but he chooses instead to remain unemployed and wait for the government job. In the meantime, he collects $500 per month in unemployment benefits (for 12 months). a) [10 marks] Assume that the government job lasts two years, that his private sector job alternative would last just as long as his spell of unemployment and public employment (i.e. would last 3 years), that salaries are constant, that the interest rate is 10 percent per year, and that leisure has no value to George. Determine the minimum public sector premium that must exist for George s decision to be rational. This question involves the calculation of discounted net present value. We evaluate the benefits associated with each option. If George decides to queue for the government sector job, the annual benefits are: 12*500 for year 1, 12*Yg for year 2, and 12*Yg for year 3, where Yg represents the government salary, which is presumably higher than the private-sector salary of $2,500 per month. (Otherwise no one would queue for them.) If George decides to take the private-sector job, the benefits are: 12*2500 for year 1, 12*2500 for year 2, and 12*2500 for year 3. The factor of 12 converts a monthly income into an annual one. All figures in years 2 and 3 have to be discounted by the rate of interest, which is 10%. The sum of the benefits from the government job are: 12* *Yg/(1 + r) + 12*Yg/(1 + r) 2. The sum of the benefits from the private-sector job are: 12* *2500/(1 + r) + 12*2500/(1 + r) 2. Since we are given a value for r of 0.1, we can input that into the equation. The total benefits from the private-sector job are: 12*2, *2,500/(1.1) + 12*2,500/(1.1) 2 = $ 82,066. The total benefits from the government job are: 12* *Yg/(1.1) + 12*Yg/(1.1) 2 = 6, *Yg/(1.1) + 12*Yg/(1.21) 6

7 = 6, *Yg + 9.2*Yg = 6, *Yg. Now equate the values of the two options and solve for Yg. We obtain a value of $ 3,784 per month. If George can receive a salary greater than that amount (which is his reservation wage for the government job), it will be worth waiting for that job, and it is rational to turn down the private-sector job. The premium works out to be $3,784 2,500 = $1284. b) [15 marks] How would your answer to part a) change if George values his leisure time? Explain. The public sector monthly premium would be lower than $1284. If George values his leisure time it is as if he is receiving unemployment benefits of more than $500 per month. If we were to redo the calculation tacking on another $250 per month (for example) on to his unemployment benefits to capture the value he places on leisure, we would find that the premium would fall. End of Exam 7