Consider a firm with production function given by q = f(E, K) = E^(1/4)K^(1/4), where E...

Consider a firm with production function given by q = f(E, K) = E^(1/4)K^(1/4), where E is number of workers and K is capital. The price of labor is w = 4 and price of capital is r = 8. The price of the output that firm produces is 20. The firm can adjust both its inputs.

1) Derive an expression for MRT S for this firm.

2) The firm wants to produce q0 units of output. What would be cost-minimizing combination of inputs (E, K) to produce q0 units of output. Note that this combination would be a function of q0.

3) Firm wants to maximize its profits. What is the profit maximizing level of inputs? How many units of output are produced? What is the firm’s profit if it produces at this optimal?

4) Consider a change in price of labor, such that w = 2. What would be the new optimal levels of both inputs? How does quantity of output produced change?

5) Decompose this change in inputs from part (3) to part (4), into scale and substitution effects

Expert Solution

Rahul Sunny answered 1 year ago

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