ECON 6912 – Assignment 3- 103 points Fall 2014
Due Monday, November 3
1. AlwaysSure is the only theft insurance company in the city. Herb is the only seller of AlwaysSure insurance products. He is desperately trying to meet his monthly sales quota. He only has time to make one more sales call. Jennifer and Johnny are the same age, live in the same street, and with identical family responsibilities. Both have a probability of robbery of 0.10. Both Jennifer and Johnny have a wealth of 900 if they are not robbed. In case of robbery, they will lose 500 units. They are only different in their utility functions. Their utility functions over wealth (X) are:
Jennifer: U(X) = 10X1/2
Johnny: U(X) = 10X1/4
a.) (3) Calculate the Pratt measure of risk aversion for both Jennifer and Johnny.
b.) (3) Who should Herb call? Why?
c.) (2) What is the “actuarially fair” premium in our case?
d.) (4) What is the maximum willingness to pay for both Jennifer and Johnny?
e.) (3) Suppose both Jennifer and Johnny are offered insurance at a price of $60? Will they be willing to buy insurance at this price? If either Jennifer or Johnny buy insurance, what is their consumer surplus?
2.a.) Read the article titled “Claim Game: The calculations behind the insurance of athletes” from The Economist: http://goo.gl/iZQ8IL. Then answer the following questions.
a.) (3) The article states that if Alex Rodriguez’s hip injury drags on it would make it harder for teams to get coverage and for athletes to get lucrative contracts in the future. Briefly explain why this is the case.
b.) (3) Suppose a team purchases a $100,000,000 policy in the event of an injury which sidelines a player for the season. Suppose this insurance costs $4,000,000. Calculate the minimum probability that the team expects an injury will happen if their utility function is given by U = W0.5 (Note: assume if the injury happens, they have a wealth of $0, and if an injury does not happen, they have a wealth of $100,000,000).
c.) (3) Suppose the insurance company that provides this insurance is risk neutral. What do you know must be true of the insurers’ expected probability of an injury happening (It must be less than or equal to __)?
d.) (3) Now suppose a player who is injured has the ability to play with one week remaining in the season. If he plays, the insurance policy does not pay anything. If he does not play, the insurance policy pays in full. What does the insurance company prefer? What does the team prefer? What does the player prefer?
e.) (3) The article states there is relatively little investigation into whether players are actually able to play or not. Given this fact, what do you think will happen (will he play or not)? What will happen to the cost of future policies as a result of this outcome?
3. The average productivity of U.S. workers are often countercyclical, which means it increases during recessions (when output decreases) and decreases during expansionary periods (when output increases).
a. (3) As an example, find what the annual change in nonfarm business labor productivity was in the first and second quarter of 2009 (during the Great Recession) and what it was during in the second and third quarters of 1994 (during an expansion) Note: the Bureau of Labor Statistics has this data readily available.
b. (3) Briefly explain how this is possible (what must be true of how L and Q change in % terms?).
c. (3) Given this fact, explain whether this means the marginal productivity of labor is generally above or below (or indeterminate) the average productivity of labor. How do you know?
4. By studying, Will can produce a higher grade, Gw, on an upcoming economics exam. His production function depends on the number of hours spent studying production problems (P) and the number of hours spent studying risk problems (R). Specifically, Gw=2.5R0.36P0.64
His roommate David’s grade production function is GD=2.5R0.25P0.75
a. (3) What are Will and David’s marginal productivity of studying risk problems?
b. (4) Calculate the marginal rate of technical substitution for both Will and David between studying the two types of problems. Interpret this at the point R=2, P=2.
c. (4) Suppose David and Will have 12 hours to study for the next exam. How much time should each spend studying risk problems and studying production problems?
5. Read the following article from The New York Times: http://goo.gl/019yj4, which discusses the migration of textile plants from England to New England (in the early 1800s), to the Carolinas (in the early 1900s) to Asia (in the early 1990s), now back to the Carolinas today.
a.) (3) After reading the article, briefly explain why some textile plants are moving back to the U.S. from Asia, despite the fact that labor costs are substantially higher in the U.S.
b.) (3) On the same set of axes, depict three separate isoquants associated with producing a given amount of textiles (let’s say 1,000,000 shirts) for the following location/time periods: 1) 1980s – Carolinas, 2) 1990s – China, 3) 2010s – Carolinas.
c.) (3) What input combinations (relative amounts of K and L) does a plant owner choose on each of the three isoquants that you have graphed? You can indicate these relative points on your graph or just compare (K/L) for each country/time period [what is true of (K/L) 1990s; (K/L)1990s; (K/L)2010s]. Note: absolute amounts don’t matter, but you can infer the relative amounts of K and L based on the information in the article.
6. Suppose a firm’s production function is given by:
Q = K*L – 0.8K2 – 0.2L2
a.) (8) Suppose K=10 in the short run; graph the total and average productivity of labor curves on the same axes. At what level of labor does average productivity reach a maximum? At what level of labor does total productivity reach a maximum?
b.) (2) Does the production function exhibit increasing, decreasing or constant returns to scale?
7. Suppose a firm has a production function in two separate plants equal to Q = K0.3 L0.5.
In plant A: K is fixed at 700, r=$20, and w=$25;
In plant B: K is fixed at 200, r=$50, and w=$5.
a) (3) Calculate the short run total costs and marginal costs in both plants as a function of Q.
b) (3) Suppose the firm has to produce 20,000 units in total. How much should they produce in both plants?
c) (3) What are the total costs in each plant? What are the marginal costs in each plant for the last unit?
8. (6) A bottling company uses two input to produce bottles of the soft drink Sludge: bottling machines, K, and workers, L. The isoquants have the usual convex shape. The machine costs $1,000 per day to run; the workers earn $200 per day. At the current level of production, the marginal product of the machine is 200 bottles per day, and the marginal product of labor is 50 bottles per day. Is this firm producing at minimum cost? If it is minimizing cost, explain why. If it is not, explain how the firm should change its ratio of inputs.
9. In the 60 Minutes Video on technological unemployment, a plant manager at Amazon said that “Each [robot] can produce the same amount as 1 ½ workers.”
a.) (3) Suppose robots and workers are perfectly substitutable inputs. Write an equation for the plant’s production function that accurately describes what the plant manager says.
b.) (2) Given your production from a., if the cost of labor is $1,000/week and the cost of capital is $2,000/week, how many workers and how many robots will the plant use to produce 60,000 packages?
c.) (2) Given your production from a., if the cost of labor is $1,500/week and the cost of capital is $2,000/week, how many workers and how many robots will the plant use to produce 60,000 packages?
10. (12) Suppose a U.S. apparel manufacturer is considering moving its production abroad. Its production function is Q=L0.7K0.3 (based on Hsieh, 1995). In the U.S., w=$8 and r=$3. In Asia, the firm would pay w=$4 and r=$4. Suppose it plans to produce 1,000 units.
a. What are the optimal amounts of L and K in each country?
b. What are their total costs in each country?
c. What would the cost of production be in Asia if the firm had to use the same factor quantities as in the U.S.?
d. Suppose the firm sells all clothes it manufactures in the U.S. What besides labor and capital costs will the firm consider in deciding whether to move production to Asia or keep production in the U.S.?