Let O(L, K) = (L³/²)*K¹/²
a. Derive demand functions for labor and capital. Then draw the labor demand curve
assuming Q = 10,r = 10. Justify the slope of the demand curve using derivatives.
B. From now on, only assume r = 20, W = 60. Derive the long-run total, average, and
marginal cost functions (should depend on Q only). Then, for Q = 5, find the cost-
minimizing bundle and calculate the long-run total cost. Write down the isocost equation.
C. Now assume the short-run scenario - capital is fixed at 25. Derive the short-run total cost function (should depend on Q only). Then, for Q = 5, find the input bundle and calculate the total cost. Write down the isocost equation.
D. Use an optimal choice diagram (isoquants and isocost lines) to graphically illustrate your optimal input bundles from parts b and c. Please label all lines/curves, clearly indicate the isocost intercepts and two bundles.