Hw 2 Solutions

ECON 450 – HW 2

The Rules: • This part of the quiz is due next Wednesday, May 20 in class. •

Quizzes turned in late will be penalized in proportion to the cost imposed on me. If I am not inconvenienced, I won’t impose a penalty.

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Make sure you put your name on the document you turn in.

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You may work with others in class; however, you are to turn in your own quiz and include the names of all others who worked with you.

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The assignment you turn in should appear professional. Graphs may be drawn by hand, but the rest of your assignment should be typed, papers should be stapled (or otherwise bound), and your answers should follow the order of the questions.

(1) In order to file a lawsuit, the plaintiff must hire a lawyer. If the suit is successful, the plaintiff will win a judgment of 6; otherwise he gets nothing. Assume the plaintiff is interested in maximizing the expected net monetary payoff -- note: E(net monetary payoff ) = psuccess ( judgement success feesuccess ) + (1 psuccess )( judgement fail fees fail )

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Assume that if the lawyer tries hard the success will be successful with probability .5, and if the lawyer does not try hard the suit will surely fail. Assume that the lawyers utility function is w e where w is the fee (which cannot be negative) and e is effort. Assume e = 1 if the attorney tries hard, and e = 0 if not. Further assume that the lawyer will only agree to take the case if her expected utility is nonnegative. (a) Suppose the plaintiff can !observe the lawyer’s effort. What is the optimal contract (i.e., what fee will the plaintiff off if effort is high; what wage will the plaintiff offer if effort is low)? With this contract, is hiring the lawyer worth it? (i) What is the maximum the plaintiff is willing to pay for high or low effort

Expected Value to Plain High Effort = .5(6 " w high ) + .5(0 " w high ) # 0 3 " w high # 0 w high $ 3 Expected Value to Plain Low Effort = 0 " w low ) # 0 "w low # 0 w low = 0

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(ii) What is the minimum amount the lawyer is willing to take for high or low effort?

ECON 450 – HW 2

U High = w high "1 # 0 w high # 1 U Low = w Low " 0 # 0 w Low # 0

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As long as the plaintiff offers an amount greater than or equal to 1, but less than or equal to 3 in exchange for high effort, the parties will agree to pursue the case.

(b) Now, suppose that the effort cannot be observed, but fees can by made contingent on the suit’s success. What is the optimal contract in this scenario? Is it worth hiring the lawyer? The wages offered by the plaintiff must be sufficient to induce the lawyer to take the case, put in high effort, and still have a positive expected value for the plaintiff. That is, they need to satisfy

.5( w win "1) + .5( w lose "1) # 0 .5( w win "1) + .5( w lose "1) # w lose " 0 .5(6 " w win ) + .5(0 " w lose ) # 0 Solving the first two equations, yields:

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w win " w lose + 2

We could try and simplify this further, but the algebra gets complicated, the simple thing to do at this point is to recognize that if we assume that w lose " 0 (as seems reasonable), then w win " 4 . Solving the third equation yields: 6 " w lose

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# w win!

These two conditions yield a range of possible agreement. ! (2) Suppose a coal mine’s workers can dig two tons of coal per hour and coal sells for $10 per ton.

(a) What is the value of a coal miner’s marginal product? 2 tons per hour * $10 per ton = $20

ECON 450 – HW 2

(b) Assume the coal mine is the only employer of miners in the area and faces a labor supply curve of the form L = 50w. The total wage bill for this firm is wL = L2 /50 . When monopsonists hire additional miners they affect the wage. The marginal expense of hiring miners is L / 25. Solve for the wage and number of workers hired by the mine company. ! Solving the monopsonist problem has two steps: Solve for quantity of labor using marginal expense = VMP Solve for wages by plugging quantity of labor in to equation for supply curve L/25 = 20 L= 500 W=500/50 = $10 (c) If the market were competitive, how many workers would be hired and at what wage? Recall that in a competitive labor market w = VMP W= $20 20 = L/50 L=1000 (d) Suppose the price of coal rises to $15. How would this affect the monopolist’s hiring and the wages of coal miners? Would the miners benefit fully from the increase in the value of their marginal product? Using the steps from part (a), w = $15 and L=750 The VMP increased by $10 ($15/ton * 2 tons per hour = $30, $30-$20 = $10); however workers only get $5 of this increase so unlike a competitive market changes in VMP do not entirely accrue to workers. (e) Now suppose that the miners form a union. Assume the firm’s marginal revenue product for labor curve is given by MRP = 70 - .1L. If the union acts as a monopoly supplier of labor, they collect a “marginal revenue” from supplying an additional worker of 70 - .2L (notice that like the MR curves of a normal monopolist this curve has twice the slope of the demand curve). The union can pursue 3 different goals

ECON 450 – HW 2

a. Force the mine to the competitive solution (S = D) b. Maximize the total wages paid c. Maximize the economic rent (or surplus) earned by the union – i.e., act as a monopolist Solve for the wages and quantity of labor associated with each of these possible outcomes. Is it obvious when of these options the union should pursue? The competitive solutions solves S = D or L/50 = 70 - .1L L = 583 W=$11.67 To maximize total wages paid the union wants to set the marginal change in total wages paid equal to zero. That is, they solve 70 - .2L = 0 L = 350 W = $35 If the union wants to maximize its economic rent, it solves the monopoly solutions using steps similar to the ones we used for the monopsonist in the first part. Set MR = MC 70-.2L = L/50 L=318 W=$38.18

(f) Compare the possible union outcomes with the monopsonist outcome. When a monopsonist firm meets a monopolist union, how will wages and employment be determined? The union outcome all have higher wages than the monopsonist outcome. When two entities with market power collide the result will not be determined using the usual rules. Instead, the observed wage and level of employment will be the result of bargaining between the firm and union. The different groups bargaining positions and their bargaining skills will ultimately determine the outcome. (3) Consider the following quotation: “The theory of compensating wage differentials is based on the assumption that workers are able to command higher wages in higher-risk jobs. While I believe that this is true in unionized sectors such as iron workers, construction workers, and lumber and sawmill workers, I have

ECON 450 – HW 2

found the opposite to be true in nonunion, nonorganized industries. In the nonunion chemical industries, as well as in such industries as soap making, etc., it has been my experience that the most dangerous jobs were handled by the lowest-paid, least educated, and usually minority workers. I am concerned about this because of the steady decline in the percentage of jobs that are covered by union contracts in this state over the past 20 years.” Please answer the following two questions about the above quotation: (a) Why might the presence of unions help to create compensating wage differentials for risk? I can think of a couple of reasons for why unions may help to create compensating wage differentials for risk. First, if there is imperfect information about a job’s risks, the union may help gather and disseminate information about the risks which could lead to workers demanded higher CWDs. Second, when negotiating with a union, the firm no longer faces the risk reward preferences of the marginal worker, rather they face the risk-reward preferences of the union. As such, unions may demand higher CWDs for risk. (b) If the lowest-paid, least-educated workers in the nonunion sector do the dangerous work, does this suggest that compensating wage differentials in the nonunion sector do not exist? Why or why not? No, it does not suggest that CWDs do not exist. Identifying CWDs requires comparing the wages at a risky job to the wages the same worker would earn on a non-risky job. It is highly plausible that these low-paid, low educated workers would earn even less in a different, less risky, job. (4) Ricardo is working at a job that pays $25,000 per year. He is contemplating a 1-year training course that entails costs of $4,000 for books and tuition. Ricardo estimates that the course will increase his income to $30,000 in each of the 3 years following completion of the course. At the end of those 3 years, Ricardo will stop working. The current interest rate is 5 percent. Is it economically rational for Ricardo to enroll in the course? Ricardo wants to enroll if the net present value of the investment exceeds the net present value of the costs. The benefit of the investment is higher income $5000 in each of 3 years. The cost of the investment is the cost of tuition and the opportunity cost of the time spent pursing the training. If we assume that Ricardo stops working while pursuing the training, the costs of the program are $4000 in tuition plus $25,000 in opportunity costs.

ECON 450 – HW 2

At this point, it should be painfully obvious that this is a bad investment. The total value of the benefits (without even calculating a present value) are substantially less than the costs of the program ($15,000 < $29,000). I think I intended to type that the after program wage was $35,000 (and not $30,000). With an after training wage of $30,000 the question is more complicated. Is $30,000 in future earnings worth foregoing $29,000 today. To figure this out, we want to compare the net present value of the benefits against the net present value of the costs:

$10,000 $10,000 $10,000 $29,000 + + " ? 1.051 1.05 2 1.05 3 1.05 0 $27,232.48 < $29,000 => Bad investment

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