Econ 633/733: Advanced Microeconomics Final Exam, Autumn 004 Professor Kosteas Name: Instructions: You will be assigned a number. Write this number in the top right corner of every page. Do not write your name on any other page except for the cover page. You have 1:50 to complete the exam. Take your time and show your work. Good Luck. Short Answer Multiple Choice Short Essay Total
Short Answer (46 points): Show your work and label any graphs. ρ ρ 1. Given the production function y = ( l + k ) ρ, what is the technical rate of substitution, the elasticity of substitution, and the returns to scale when ρ = 0.5? (8 pts) 1
1/. A price taking firm has the production function Y = L K its output is p=$10. 1/. The market price for a) If the firm s capital stock is fixed at K = 9, derive the firm s demand for labor function. If the wage rate is w = $3, how much labor does the firm hire? ( 3 pts) b) Now assume the firm is in the long-run. Given that w = $3 and r = $6, derive the firms total cost function. (5 pts)
3. A firm has two plants with cost functions c 1( y1) = 4y1 and c ( y ) = y + 8. What is the cost function for the firm? (6 pts)
4. There is a competitive industry with an infinite number of potential firms. All firms have the same cost function c ( q) = q + 4. Industry demand is Q = 100 5p, where Q is total industry output and p is the output price. Let n denote the number of firms in the industry. Find the long-run equilibrium number of firms (n), price and quantity produced by each firm. (8 pts)
5. Suppose there is a pure exchange economy with two consumers (Andrew and Hilary) α 1 α and two goods (x,y). Further, suppose Andrew s utility is U A = x A y A while Hilary s α 1 α utility is U H = xh yh. Finally, Andrew s endowment is w A =(1,4) while Hilary s endowment is w H =(3,). Find the equilibrium price ratio. What happens to the relative price of good y when α increases? (8 pts)
6. Firm 1 produces output Q 1 which it sells at price p 1 =100. Firm 1 produces output Q which it sells at price p =00. The respective cost functions are C = and C Q 5 = 10 Q. 1 a) What type of externality does this example illustrate? (1 pt) 1 0Q 1 b) What are the socially efficient levels of Q 1 and Q? (5 pts) c) If firm 1 is not responsible for the externality, how much will it produce? ( pts)
II. Multiple Choice ( points each): Circle the correct answer. 1. Given diminishing marginal returns and that the firm is a price-taker in the input market, if marginal revenue product is less than marginal factor cost, the firm should. A) increase input use B) keep input use constant C) decrease input use D) cannot tell from information given.. Linda wants to open a T-shirt stand for Homecoming week. The school will license her a booth for $100. Each T-shirt from the store will cost her $4. Linda's average cost function will be: A) $100 + $4 * X B) $100 / X + $4 C) $104 / X D) $100 / X + $4 / X 3. Using diagram 11., suppose that the initial equilibrium price (S = D) is $10. The government decides to impose a $5 tax on suppliers. The economic incidence of the tax would be that suppliers would receive a unit. A) $10 B) $1 C) $7 D) $5 4. Using diagram 11., suppose that the initial equilibrium price (S = D) is $10. The government decides to impose a $5 tax on suppliers. The statutory incidence of the tax would be that suppliers would receive a unit. A) $10
B) $1 C) $7 D) $5 5. Private firms have little incentive to produce a nonexcludable public good because: A) the social benefit is less than the private benefit B) the social benefit is less than the social cost C) the social cost is different than the private cost D) the free-rider problem arises 6. A firm has only two inputs, iron and steel. Suppose that steel is the fixed factor in the short-run. The firm's short-run total cost curve: A) does not depend on the level of steel B) shifts upward as the level of steel increases C) has its slope increase as the level of steel increases D) shifts downward as the level of steel increases 7. Production functions provide measures of output. Utility functions provide measures of utility. A) cardinal : cardinal B) cardinal : ordinal C) ordinal : ordinal D) ordinal : cardinal 8. A possible explanation for decreasing returns to scale is: A) increasing output from experience B) the specialization capability of large firms C) managerial problems with control D) All the above
9. Using diagram 1.1, given the budget constraint B1, the quantity supplied of oranges: A) is greater than the quantity demanded B) is equal to the quantity demanded C) is less than the quantity demanded D) cannot tell from information given. 10. Using diagram 1.1, the initial budget line is given as B1. In this situation, the price of apples is and the price of oranges is. A) too low : too low B) too low : too high C) too high : too low D) too high : too high 11. A product sells for $8 in the current period and $11 in the next period. Hiring an additional worker will increase output by 5 units each period. If the interest rate is 10%, the present value of the marginal revenue product of labor is: A) $95 B) $90 C) $55 D) $100.50 1. One benefit from using taxes instead of regulation to internalize extermalities is: A) choosing the proper tax is easier than choosing the proper regulation B) taxes are more efficient C) taxes provide incentive for firms to adopt methods to reduce an externality. D) all of the above
1. What are the traditional theories used to explain firm boundaries? What are the shortcomings of these theories? How can they be explained?. What is contingent valuation and how is it used? What are the shortcomings of this method compared to other approaches? 3. Funding for public goods is usually raised through distortionary (non-lump sum) taxes. How does this affect the efficient level of the public good? How have economists addressed this issue?