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- Q9 Suppose capital costs $10 per unit and labour costs $5 per unit. For a profit-maximising firm operating at its optimal factor mix, if the marginal product of capital is 50, then the marginal product of labour must be... a. 25. b. 50. c. 100. d. 20. e. 10.Suppose that the production function of the firm is:Q = 100L1/2.K1/2K= 100, P = $1, w = $30 and r = $40. Determine the quantity of labor that the firm should hire in order to maximize the profits. What is the maximum profit of this firm?Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L − L2/(23*100), where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $5 per hour (wage plus fringe benefits). The firm faces the fixed selling price, P = $40. How much labor should the firm employ? (Round your answer to the nearest whole number.)
- 7. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What are the demand functions for labor 1(v,w.p) and capital k(v,w,p)? [Show your work] 8. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What is the supply function q(v,w,p)? [Show your work]A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. The production function is given by: Q=60L-2L^2+180K-3K^2, where Q is total output. Determine the firm's optimal combination of capital (K) and labor (L)?Suppose a firm’s conditional factor demand functions (the inputs needed to produce q at minimum cost with prices w and q) for labor and capital are given by L(w, q, r) = 4rq and K(w, q, r) = 4wq . What is its total cost function?
- Suppose the firm is hiring labor and capital and that the ratio of marginal products of the two inputs equals the ratio of input prices. Does this imply that the firm is maximizing profits? Why or why not?Suppose that John is a shrubber. As a master shrubber, he hires apprentices, L, at wage w and purchases capital, K, (electric shrubbery trimmers, for example) to create his high-end shrubberies. Capital is expensive, so he generally borrows money to purchase the equipment. The cost of capital is r. John can produce shrubberies according to the production function q = 10 · K^1/4 L^1/4. We can assume John is a price taker. If wages are $10/hour, the cost of capital is $40/hour, and shrubberies sell for p = $160, how many shrubberies will John produce and sell? How much labor and capital will he purchase to produce that output? What are his profits?In each of the following four cases, MRPL and MRPC refer to the marginal revenue products of labor and capital, respectively, and PL and PC refer to their prices. Indicate in each case whether the conditions are consistent with maximum profits for the firm. If not, state which resource(s) should be used in larger amounts and which resource(s) should be used in smaller amounts. a. MRPL = $8; PL = $4; MRPC = $8; PC = $4. b. MRPL = $10; PL = $12; MRPC = $14; PC = $9. c. MRPL = $6; PL = $6; MRPC = $12; PC = $12. d. MRPL = $22; PL = $26; MRPC = $16; PC = $19.
- Suppose that the process of producing mozzarella sticks is described by the following production function: Q = KL^2. If the price of renting shaping machine is $10 and the price of hiring labor is $15. What is the capital output ratio?The least-cost rule states that a firm should employ labor such at the marginal product per dollar spent on labor is equal to Multiple Choice the marginal product per dollar spent on capital. the wage rate. the marginal cost of labor. the marginal product of labor.Suppose a competitive firm is paying a wage of $12 an hour and sells its product at $3 per unit. Assume that labor is the only input. If, hiring another worker would increase output by three units per hour, then to maximize profits the firm should not change the number of workers it currently hires. not hire an additional worker. hire another worker. There is not enough information to answer the question.
