Question 6. Firm theory (a) For a firm, 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 firm sells its 43 goods for P = 5 apiece. The cost of a unit of capital is R = 0.2 and the firm has K = 75 capital. The firm's profit is π = 0. It has L = 10 workers. What is the wage W? What are its units? (c) Yet another firm has a production function Y = K0.25 L0.75, the MPK 0.25 (1) and the firm is stuck with L = 10. The price of the good is P = 5. The cost of capital is R = 0.2. What is the profit-maximizing volume of capital? = 0.75 (d) If the economy's output follows the production function Y = K0.33L0.67 and the output is 30 (and we assume it equals to the national income), how much does the population receive in wages? Show work.

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Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.