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21011samplemidterm

21011samplemidterm - Department of Economics University of...

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Department of Economics University of California, Irvine 210A - Microeconomic Theory I Fall 2011 Sample Midterm Exam questions (An exam usually consists of three questions like those below) 1. Consider a production function f ( x 1 ; x 2 ) , whereby output is produced with two inputs. a. De°ne the isoquant for this production function. b. Find su¢ cient conditions that would guarantee the convexity of the isoquant. 2. a. De°ne the pro°t function in the neoclassical theory of the °rm. b. Prove that the pro°t function is convex in prices. 3. Consider the technology described by f ( x ) = 0 for all x ° 1 and f ( x ) = ln x for x > 1 : a. Derive the conditional factor demand function and the cost function for this technology. b. Con°rm three properties of the cost function, including Shephard±s Lemma. 4. a. De°ne the cost function in the neoclassical theory of the °rm. b. Prove that the cost function is concave in prices. c. Show the properties of negativity and symmetry for conditional factor demand functions.
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