W14 MIC Problem Set 5 Solutions

Substituting this information into i q 13 13 13 k 27k

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Unformatted text preview: iii) tell us that L = M = 27K. Substituting this information into (i), Q = 1/3 1/3 1/3 K (27K) (27K) = 9K, The input demand for capital is therefore K = Q/9. The input demands for labor and raw material will be L = M = 27K = 27(Q/9) = 3Q. Thus, L = M = 3Q . Total expenditure: C = rK + wL + mM = 27(Q/9) + 1(3Q) + 1(3Q) = 9Q. The long run total cost function is therefore C(Q) = 9Q. c) The input demand for labor can be found using the production function directly because there is only ONE variable factor. Simply plug in the given values of K and M to get a production function based only on L, which can be solved in the form L[Q]: 1/3 1/3 1/3 1/3 1/3 1/3 1/3 3 Q = K L M = (1) L (8) = 2L . Thus L = Q /8. 3 3 Total expenditure: C = rK + wL + mM = 27(1) + 1(Q /8) + 1(8) = 35 + Q /8. 3 The short run total cost function is therefore C(Q) = 35 + (Q /8). 3) A firm produces Q units of output using K units of capital and L units of labor. ! L$ a) Suppose the production function is Q = min " K , % . The factor prices are r = 8 (for ca...
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This homework help was uploaded on 03/03/2014 for the course ECON 310 taught by Professor Whinston during the Spring '12 term at Northwestern.

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