Suppose that you have the following production function: ? = (100?^1/3)*(?^2/3) Where k represents the units...

Suppose that you have the following production function: ? = (100?^1/3)*(?^2/3) Where k represents the units of capital employed at production, L is the number of labor hours employed for total production. The wage rate equals to $18 per hour. The cost of capital equals $2,000 per unit.

a) What are the returns of scale for this production function? Prove it

b) You are currently employing 100 hours of labor. Calculate your total costs, average cost and marginal costs of labor and capital if K=100 units.

c) Which input is more productive? Should you employ more labor or more capital?

d) Draw the production function, MPK and MPL for the different values of K and L.

Expert Solution

Figure 1 (Production Function)

Figure 2 (MPL and MPK)

Rahul Sunny answered 1 hour ago

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