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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.
 Spring '12
 Whinston

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