A US electronics firm is planning to build a plant in a foreign country and hires you to make some calculations. The technology of the plant is given by the production function. The price of capital and labor are:

and.

a) (8 pts.) Find the equation for the firm's long-run total cost curve as a function of quantityq.

b) (5 pts.) Derive the equation for the firm's short-run total cost curve as a function of quantity when capital is fixed at a quantity of 4 unit (i.e., K =4).

c) (7 pts.) Graph the short-run cost curve together with the long-run cost curve. For what value of production the short-run will be as efficient as the long-run?