(a) Lothian Company has estimated the following production function for its product

Q= 10 K ^0.3 L ^0.7 where Q represents units of output, K units of capital, and L units of labor.What is the coefficient of output elasticity? What are the returns to scale?

(b) Suppose that a firm's total cost equation is TC = 10,000 + 100Q+ 25Q² where TC is total cost and Q is the level of output.

(i) What output level will minimize the firm's average total cost?

(ii) Calculate the average and marginal cost at the average cost minimizing output level.

Suppose that an investment opportunity, which requires an initial outlay of $100,000, is expected to yield a return of $250,000 after 30years.

(i) Will the investment be profitable if the cost of capital is 7%?

(ii) Will the investment be profitable if the cost of capital is 2%?

(iii) At what cost of capital will the investor be indifferent to the investment?