Question 6. Firm theory (a) For a rm, the marginal product of capital is 3.5. This year, its output decreased by 14 units from last year and its capital is 43. What was its capital last year? (b) Another rm sells its 43 goods for P = 5 apiece. The cost of a unit of capital is R = 0.2 and the rm has K = 75 capital. The rm's profit is n = 0. It has L = 10 workers. What is the wage W? What are its units? 0.75 (0) Yet another rm has a production function Y = K 0'25L0-75, the MPK = 0.25 (i) and the rm is stuck with Z = 10. The price of the good is P = 5. The cost of capital is R = 0.2. What is the prot-maximizing volume of capital? (d) If the economy's output follows the production function Y = K 0'33L0-67 and the output is 30 I (and we assume it equals to the national income), how much does the population receive in wages? Show work