UNIVERSITY OF WASHINGTON Department of Economics. Economics 200. Problem Set Consider the two investment projects described in the table below.

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1 UNIVERSITY OF WASHINGTON Department of Economics Economics 200 Scott 1. Consider the two investment projects described in the table below. a. If the interest rate is 25%, what is the net present value of project A? (Give the numerical value.) b. What is the internal rate of return for project B? (Give the numerical value.) 2. A firm is considering an investment project that costs $1000 now and returns $70 at the end of one year from now, two years from now, and so on at the end of each year forever. Thus, the investment is a perpetuity that pays $70 each period. a. If the interest rate is 5%, what is the net present discounted value of the project? Explain, showing your work beginning with the pertinent infinite summation of terms and solving for the capitalized value of the asset. b. What is the internal rate of return on the project? Again, explain, showing your work. c. Should the firm accept the project? Explain, using the information from both parts a and b in your explanation. d. Suppose that the government introduces a new tax that cuts the investment's return in each period from $70 to $35. Will the project be accepted now? Explain by using both net present value and the internal rate of return. 3. A homeowner is considering purchasing new energy-saving water heater, which costs $700 and would save them $120 per year on their electric bill. The water heater will last at least one year with probability 0.9 (i.e. 90% chance of lasting one year). If the heater lasts one year, there is again a 90% chance it will last until the end of a second year. If it lasts a third year, there is a 90% chance it will last a fourth, etc., forever. If the homeowner would need to cash in a $700 certificate of deposit (CD) that earns 5% per year in order to buy the water heater, is it worth doing? Explain.

2 Economics Scott For questions 2 and 3, refer to the following results: Suppose 0< <1, so that is very small for very large. (1) Let = (2) Then, = (3) Subtract (2) from (1) to see that 1 = 1, or = 1 1. Suppose the interest rate is (annual, compounded annually). If a perpetuity pays some amount after 1 year, after 2 years, again after 3 years, after 4, etc., forever, then the present discounted value of this perpetuity at time 0 (one year before the first payment accrues) is = = = Suppose now that there is some risk that this perpetuity stops at some point. Specifically, say the probability of getting that first payment is, and the probability of getting at least one more payment, conditional on having gotten the last, is also. In other words there is a constant probability (or hazard rate, if you like), equal to 1, that any given payment will be the last. In this case, the value of the perpetuity is the following: = = 1 1+ = 1+ Notice that, if =1, =, so all you have to remember is!

3 Economics Scott 4. The Efficiency of Competitive Equilibrium A former central planner in the former Soviet Union observed the rush toward market-based economic reforms and lamented, In the past, the government decided how much of each good to produce. Even then, with our best intentions there were long lines of consumers confronted with empty shelves for some products while at the same time other products piled up unwanted. If our careful planning could not solve the problem of allocating resources so as to produce the right mix of output, how could an unplanned market economy possibly succeed? Follow the outline below to explain why the general equilibrium of a competitive market system provides an efficient mix of output: a. Your answer should begin by stating what economists mean by efficiency in general that is, give the name of the condition for efficiency and explain its meaning. b. Then state and explain (explain why the condition that you state must be true) what must be true about the MRT and the MRS for any two goods X and Y if in fact the economy s output mix is to be efficient. c. Then explain why the condition stated in part b will in fact hold in a competitive general equilibrium. 5. Consumer Equilibrium Yesterday, for the customers who bought goods X and Y at Whole Foods, the marginal rate of substitution for goods X and Y was 2; while for the customers who bought those same goods X and Y at Safeway, the marginal rate of substitution for goods X and Y was 3. a. Explain completely why this difference resulted, using appropriate graphs of consumer equilibrium to accompany your prose explanation. b. Given the situation described in part a, was the consumption of goods X and Y efficient? Explain. 6. Monopoly Problem 2 on page 286 of the text.

4 Economics Scott 7. Monopoly In the diagram below it appears that the profit-maximizing monopolist makes zero profits (just as a perfect competitor would) by producing and pricing where her MR = MC at A. She could apparently make positive profits by producing at B where MC exceeds MR. Explain the paradox. 8. Monopoly A reclusive leader of an out-of-the-wacertain tape recordings, the demand for which is given by the equation: P = 10 - Q. kingdom has exclusive rights of ownership to a. Derive the TR schedule, write its equation, and sketch the MR curve. b. The leader, having connections in the recording industry, is able to produce these tapes at zero costs. What is the profit-maximizing P and Q? c. His economic advisor, Greenspan, suggests that he simply revenue maximize in this situation. Do you agree? d. The leader s connectionn in the record industry is convicted of attempting to bribe high officials, and the leader is forced to buy his tapes at a marginal cost of MC = 3Q. Now what is the profit-maximizing P and Q? e. Are profits higher in (b) or (d)? Explain why you don t need to know about AC here, while you usually do when speaking of profits.

5 Economics Scott 9. Regulation: Having just discovered that the ATT Co. has a monopoly on the telephone industry, the government is considering three alternative methods of regulation: a. A unit tax on each telephone call. b. A yearly franchise fee (i.e. a lump sum tax). c. A price ceiling. Which method would you support and why?