Unformatted text preview: ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission University of Toronto, Department of Economics, ECO 204, Summer 2009. Ajaz Hussain Midterm Test PLEASE FILL OUT THE INFORMATION BELOW Please write your name as it appears in ROSI: LAST NAME: FIRST NAME: MIDDLE NAME: U Toronto ID #: SIGNATURE: (FOR PROCTOR) ID CHECK ________ SCORES Question 1 2 3 4 5 6 7 Out of 5 15 15 20 10 5 30 TOTAL SCORE (OUT OF 100) Score This test consists of 7 questions. For your convenience, there is a worksheet at the end of this test. There are a total of 16 pages including the cover page and worksheet. Keep your answers brief. Good luck! 1 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission Question 1 (5 points) Suppose a consumer has the utility function U = Q11/4 Q23/4. Does the utility function: U = {Q11/4 Q23/4}2 represent the same preferences as the utility function U = Q11/4 Q23/4? Explain briefly. 2 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission Question 2 (15 points) You're trying to figure out a consumer's preferences and notice that regardless of income or prices, she always spends 10% of her income on good 1, 20% of her income on good 2, 40% of her income on good 3 and the remainder of her income on good 4. (a) (5 points) Can you guess what her utility function is? Explain briefly. (b) (5 points) What is the demand equation for good 3? Show all calculations. 3 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission (c) (5 points) What are the income and price elasticity of good 3? Show (any) calculations. 4 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission Question 3 (15 points) A consumer perceives four "good" goods as complements. Assume prices are uniform and, along with income Y, are given. (a) (5 points) Derive the demand function for good 2. Show (any) calculations. (b) (5 points) What is the elasticity of good 2 with respect to the total price of all goods? 5 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission (c) (5 points) Suppose P1 = $10, P2 = $100, P3 = $40 and P4 = $50. What is impact on the consumption of good 2 if the price of good 2 increases by 10%? Explain your answer and show any calculations. 6 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission Question 4 (20 points) A company uses labor (L), capital (K) and materials (M) to produce output (Q). The production function is: Q = L K M where = , = and = . Suppose: PK =$10 , PL = $20 and PM = $20. (a) (5 points) Describe this company's returns (not returns to scale). Show all calculations. 7 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission (b) (10 points) Now suppose capital is fixed at k = 100. Derive the short run cost function and show that it exhibits the returns in part (a). Show all calculations. 8 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission (c) (5 points) Will the company's cost of production be affected more by an increase in wages or the price of materials? Show all calculations. 9 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission Question 5 (10 points) An individual lives for two periods (T = 1 and 2). Her real income (measured in actual output, i.e. not in $) when she's "young" in T = 1 is Y1 and her income (measured in actual output, i.e. not in $) when she's "old" in T = 2 is Y2. Let T = 1 be the base period so that P1 = 1 and allow for the possibility of inflation (i.e. it may be that P1 P2). Denote the nominal interest rate by i. Suppose this individual has CobbDouglas preferences over consumption in T = 1 and in T = 2: U = C1 C2 This individual recently won a lottery (measured in actual output). She can choose to receive the entire prize either when she's young or when she's old. That is, she can choose to have Y1 or Y2 . Which option would she choose? Show all calculations clearly. It's OK to just give not derive the relevant intertemporal budget constraint. Hint: She'll choose whichever option makes her happier. 10 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission Question 6 (5 points) A company uses labor and capital as complements to produce output with the production function q = min(L, K). Under what conditions will this company have a Ushaped long run AC (average cost) curve? Show all calculations and explain your answer. 11 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission Question 7 (30 points) A company uses labor and capital as complements to produce output with the production function q = min(L, K) + ( notice the "" here). (a) (5 points) What "returns to scale" does the company have? Show all calculations. 12 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission (b) (5 points) Solve for the optimal (long run) labor and capital demands. Show all calculations. (c) (5 points) Derive the long run cost function. Show all calculations. 13 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission (d) (15 points) Plot the AC curve (AC vs. output). If it's easier for you, make up numbers for wages, price of capital and . Hint: there is more than one curve. 14 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission ____________________________________________________________________________________________ THE END 15 ECO 204, Summer 2009, Midterm Test This test is copyright material and may not be used for commercial purposes without prior permission WORKSHEET 16 ...
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