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Econ 201 Spring 2009 Exam 2 Part 1

Econ 201 Spring 2009 Exam 2 Part 1 - ECONOMICS 201 SPRING...

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Unformatted text preview: ECONOMICS 201 SPRING 2009 EXAM 2 instructions: Please mark your answers clearly. No class notes or other materials are allowed. 100 points total. Each question is worth 5 points with the exception onuestion 3 (10 points), Question 6 (IS points), Question 13 (10 points), and Question 14 (15 points). i. Characterize the returns to scale (decreasing, constant, or increasing) associated with the following production functions. a. y = f(X],X2) = 2Xl +33“ b. y =ftX..X2) = minizXn3X2} 2. True or false: When the firm solves the PMP, and the resulting profit is greater than zero and less than infinity, it must be that returns to scale are decreasing. Explain. 3. Zeus makes planets using earth (input 1), water (input 2), and fire (input 3). The input prices of earth, water, and fire are wl , w2 , and W3 respectively. His production function is y = f(X1,X2,X3) = XfiXng. (10 points) a. What is Zeus” CMP (cost minimization problem)? b. What is the Lagrangian (use p as the multiplier)? What are the first—order conditions (FOCs)? c. Use the FOCs to show that Zeus chooses inputs such that MR???” =Input Price Rariou. 4. True or false: Suppose that a firm solves the CMP and uses lechIIOIOglr"f(Xl ,X2) = aX] + sz (perfect substitutes). Ifthe price of an input rises, the firm necessarily uses less of it. 5. True or false: Suppose that a firm solves the CMP and uses technology/(XI ,X2) = minlnXl ,le} (perfect complements}. If the price of an input rises. the firm necessarily uses less of it. 6. Dora the Explorer produces two outputs, fun (output I) and leaming (output 2). using one input,X. The output price offun is PI . and the output price oflearning is P2 . The input price oins w. Dora produces fun using the. production functionyI = (X; l , Where X1 is the amount of the input allocated to output 1. Analogously. she produces learning using the production functiony2 = [2(X2) , where X2 is the amount of the input allocated to output 2 (15 pointst a. What is Dora the Explorer‘s PMP (protit maximization problem)? b. What are the first-order conditions (with respect to X] and X 2 )'? c. Use the FOCs to demonstrate that when Dora produces both outputs, she does So such that the marginal amount ol‘input used in the production of fun yields as much revenue as the marginal amount of input used in the production ofleaming. 7. True or false: Ifthere are no fixed costs, it is not possible for the firm to make negative profits. Explain. ...
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