ECO204_2008_Test_2_solutions

# Suppose edison chang is in the long run calculate

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Unformatted text preview: /dL = L1 K + dq/dK = L K1 + MRTS = ( L1 K + )/( L K1 + ) 2 ECO 204, 2008-2009, Test 2 Solutions This test is copyright material and may not be used for commercial purposes without prior permission Question 2 (10 points) MazaMataHari has the production function q = L k. Suppose MazaMataHari is in the short run. What is MazaMataHari `s MRTS (in terms of q) at the fixed capital and optimal labor? Show all calculations clearly. Answer: Explanation: We need to derive the MRTS at k, q and the optimal short run labor. MRTS = MPL/MPK = (dq/dL)/(dq/dK) q = L k dq/dL = L1 k dq/dK = L k1 MRTS = (L1 k)/(L k1) MRTS = ( k)/( L) = (/)(k/L) The question asks for the MRTS at k and optimal L. Given q and k, the optimal short run labor is: L = (q/k )1/ = q1// k/ Substituting in MRTS yields: MRTS = (/)(k/L) MRTS = (/)(k/{q1// k/}) MRTS = (/) (k1 / /q1/ ) 3 ECO 204, 2008-2009, Test 2 Solutions This test is copyright material and may not be used for commercial purposes without prior permission Question 3 (10 points) A company uses Labor (L), Capital (K) and Materials (M) as inputs to produce target output q with the production function q = L K M. (a) (5 points) For what values of , and will this company have constant returns to scale? Show your calculations below. Answer: Explanation: A production function has constant returns to scale (RTS = 1) if: f(L, K, M) = f(L, K, M). That is, when output with all inputs scaled up by a factor is equal to the output s...
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