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- The production function of a competitive firm is described by the equation y = 2x11/2 6x21/2. The factor prices are p1 = $3 and p2 = $4 and the firm can hire as much of either factor it wants at these prices. What is the firm’s marginal cost?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?suppose that we are in there long-run and a firm is choosing K and L to cost minimize. Suppose that as in tutorial: Q = (LK)^0.5. (or also written as Q = (LK)0.5) This implies a Marginal Rate of Technical Substitution (MRTS) that is given by: MRTS = -K/L As in lecture and tutorial and the above question, assume that labour is on the x-axis. Suppose also that the price of labour is equal to $6, the price of capital is equal to $23. The firm receives an order for 222 units of output, and wants to find a way to minimize its costs of producing this output. How much capital will the firm need to use if it wants to fulfill this order and is cost minimizing?
- Consider the following shortrun production function: Q =100L - L2 where Q is the output level and L is labour input. If the price of output in the market is K.sh 50 and labour costs K.sh 1200 per hour, how many hours would the firm use to maximize profits. What is the profit maximizing level of output?Q13 Tha use of cannabis was legalized in Canada in 2017. Let's assume that the cannabis in Canada sector perfectly competitive. Assume labour is the only variable input and that an additional input of labour increases total output from 5 to 12 ounces of cannabis. If cannabis sells for $10 per ounce in a perfectly competitive market, the MRP of this additional worker is Multiple Choice $7. can be either positive or negative. $120. $70. $10.A firm produces output according to the production function . If it sells its output in a perfectly competitive market at a price of 10, and if K is fixed at 4 units, what is this firm’s short run demand function for labor? (Remember profit maximizing labor demand).
- Consider the following shortrun production function: (Q=100L- L*L), where Q is the output level and L is labour input If the price of output in the market is K.sh 50 and labour costs K.sh 1200 per hour, how many hours would the firm use to maximize profits. What is the profit maximizing level of output?True or false and explain Suppose a firm’s marginal product of labour is MPL = 10/L, where L is measured in labour hours, the price of the product is $600, and the cost per hour of labour is $30. The firm currently employs 150 labour hours. In order to maximize the firm’s profits in the short run, the manager should increase its labour employment by 40 labour hours.Goleta Brewing Company hires only two types of labor, managers and brewing assistants (denoted M and B, respectively). GBC has the following Cobb-Douglas production function F(M,B) = M.5 B.5 and wants to produce 10 barrels of pale ale this week. If the wage of managers is $50 per hour and the wage of brewing assistants is $10 per hour, how many managers and brewing assistants should the firm hire (round to nearest whole number)? How does your answer change when the wage of managers decreases to $30 per hour and the wage of brewing assistants remains constant. Is this result consistent with your intuition?
- 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 profifits 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 = $4b. MRPL = $10; PL = $12; MRPC = $14; PC = $9c. MRPL = $6; PL = $6; MRPC = $12; PC = $12d. MRPL = $22; PL = $26; MRPC = $16; PC = $19Jess owns a firm that uses labour (L) and capital (C) to sell widgets (X), according to the following production function: X = F(L,C) = ln(L) + ln(C) Jesse buys her factors and sells her output in perfectly competitive markets. The market prices for L, C and W are a, r and p, respectively. What is the firm’s profit function. What is the firm's marginal product of labour , marginal product of capital and marginal rate of technical substitution Does the firm exhibit a diminishing marginal product of capital? What is the firms demand functions for labour and capital. Say the central bank decides to increase interest rates, causing ? to go up. What effect will this have on the firm’s use of L and C? What effect will it have on output (X) and profits?If the short run production function is given by q=(1/10)lnL and the price at which the good is sold is 100 then the demand for labor L=.......... Group of answer choices a. 1/w b. 100/w c. 10/w d. 50/w e, None of the above
