ECON 311 Fall Quarter, 2009 NAME: Prof. Hamilton. FINAL EXAM 200 points

Transcription

1 ECON 311 Fall Quarter, 2009 NAME: Prof. Hamilton FINAL EXAM 200 points 1. (30 points). Consider two ways for the government to collect tax revenue: a sales tax of on clothes, or an income tax. If you currently buy both food and clothes and your total tax payment would be the same under either tax, which tax would you prefer, or are you indifferent between the two taxes? Support your answer with a diagram.

2 2. (20 points). Write out (or describe in words) the condition which must hold at a cost-minimizing input mix for a firm that employs both capital and labor in production. Show the cost-minimizing outcome on a diagram. Briefly provide intuition on why the condition you state must hold. 3. (30 points) (a) Depict an industry in long-run competitive equilibrium on a 2-panel diagram. In one panel, show the profit-maximizing output level for an individual firm. In the other panel, show market supply and market demand.

3 (b) Suppose your diagram depicts the situation of an individual firm in the U.S. selling in a global market. Now suppose an earthquake hits firms in China that compete with the U.S. firm in the global market and temporarily removes their output from global supply. Show on your diagram: (i) the effect of the supply disruption on the global market price, (ii) the short-run profit-maximizing output level of the U.S. firm, and (iii) the short-run profit level of the U.S. firm. 4. (40 points). An individual derives utility from consumption goods, X, and leisure time, N, to maximize the daily utility level, u = XN. Outside income per day is $m and the price of consumption goods is $p. The individual can earn money each day by working at a wage rate of $w per hour, but working of course takes away from leisure time (which implies it causes disutility). The individual s utility maximization problem is constrained by two things: (i) the budget constraint, px = m + wl, and (ii) the time constraint, L+ N = 24. (a) Write a single equation for the budget constraint in terms of N, X, and m and interpret. (b) Derive the demands for goods and leisure (X * and N * )

4 (c) Solve for the individual s labor supply function, L *. Graph the labor supply function and verify that labor supply slopes upward in the wage rate. (d) What is the effect of an increase in outside income (m) on labor supply? Show the effect of a decrease in m (for instance due to graduation) on the individual s labor supply. 5. (40 points). Consumer utility for calculators (x) and all other goods (y) is given by the utility 2 function uxy (, ) = 100x 1.5x + y. The price of x is $p and the price of y is $1. (a) Compute consumer demand for calculators.

5 The production function for a firm in the business of calculator assembly is given by x = 5K 0.5 L 0.5 (b) If both inputs are variable and w = $20 and r = $5, derive the cost function. (c) Using the demand and cost information above, derive the competitive equilibrium quantity and price in the calculator market. Show the competitive equilibrium on a diagram.

6 (d) If the calculator business is controlled by a monopoly firm, calculate the monopoly price and quantity of calculators in the market. Show the monopoly equilibrium on your diagram above. Shade the region that represents deadweight loss under monopoly. 6. (20 points). Suppose Nokona and Rawlings compete in a Cournot duopoly market for baseball gloves with the cost functions c(q N ) = 5q N + q N 2 for Nokona and c(q R ) = 5q R + q R 2 for Rawlings. Player s view Nokona and Rawling gloves to be perfect substitutes and inverse demand for baseball gloves is P = 85 Q, where Q = q N + q R is the total quantity of gloves produced by both firms.

7 (a) Calculate the reaction functions, q N R and q R R. Show the equilibrium quantity of gloves produced by each firm as the intersection of two reaction functions on a graph. (b) Find the equilibrium quantity of gloves produced in a Cournot duopoly. What is the market price of a baseball glove in a Cournot duopoly? 7. (20 points). Billy John Pigskin of Mule Shoe, Texas has a von Neumann-Morgenstern utility function of uc () = c. Billy John weighs 400 pounds and can outrun jackrabbits and pizza delivery trucks. Billy John is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If an injury ends

8 his football career, he will receive a $10,000 contract as a refuse removal facilitator. There is a 10% chance that Billy John will be injured badly enough to end his career. If Billy John can buy an insurance policy that pays him $1,000,000 if he suffers a career ending injury while in college at a price $p, what is the largest price that Billy John would be willing to pay for such an insurance policy? Derive Billy John s maximum willingness to pay and show this value on a diagram. THE END. Have a great winter break!