Suppose the firm faces the following (Cobb Douglas) production function: Qx = 10

Question

Suppose the firm faces the following (Cobb Douglas) production function:
Qx = 10 L^.4 K^.6
Suppose further the PL = $15 and PK = $30
TC = P (lowercase l) L (PlL) + Pk K
And
Total Costs C = $30,000.
Let Profit = %u03C0
%u03C0 = TR %u2013 TC = (P*Q) %u2013 (PL L + PK K)
a. Calculate the MPL and the MPK?
b. What is the Marginal Rate of Technical Substitution of labor for capital?
c. Determine the optimal input mix of capital to labor given the isocost line:
d. What is the level of output given the quantity of labor and capital determined in part a?
e. Suppose the price of the good produced is equal to $60/unit. Is the firm making a profit?
f. Does this production function exhibit increasing, decreasing, or constant returns to scale? Explain.

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