A competitive firm's production function is f(L, M) = 8L1/2 + 8M ¹/2. The price of L is $1 and the price of M is $3. The marginal product of L is 4/L1/2 and that of M is 4/M¹/2. The price of output is $6. What is quantity of output? the profit-maximizing 512
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- A manager hires a labor and rents capital equipment in a very competitive market. Currently the wage rate is Gh₵ 2 per hour and capital is rented at Gh₵ 5per hour, the unit price of the product is Gh₵ 0.25 and total cost is1000. Suppose the firm’s production is as follows: Q =14K⁰L⁰+10 Required What is the amount of labor and capital the firm should employ in order to maximize profit. What is the maximum profit.X and Y are factors of production. X's marginal product is 30 and Y's marginal product is 20. X=5 dollars for each unit, Y= 4 dollars for each unit. Since Y costs less than X, can the firm keep produce the same output at a cheaper cost by using less of X and more of Y? Explain why or why not.Question 5 A manager hires labour and rents capital equipment in a very competitive market. Currently the wage rate is GH¢2 per hour and capital is rented at GH¢18 per hour, the unit price of the product is GH¢0.75 and total cost is 576. Suppose the firm’s production function is as ).(+ ).,+ follows: ? = 20? ? + 15 a) what is the amount of labour and capital the firm should employ to maximize output? b) What is the maximum profit?
- Suppose that labor is the only input used by a perfectly competitive firm. The firm’s production function is as follows: Number of Workers: 0, 1, 2, 3, 4, 5, 6, 7 Units of Output: 0, 7, 13, 19, 25, 28, 29, 29 a. Calculate the marginal product for each additional worker. b. Each unit of output sells for $10. Calculate the value of the marginal product of each worker. c. Compute the marginal profit if the wage is $100 a day. 2. Your enterprising uncle opens a sandwich shop that employs 7 people. The employees are paid $12 per hour, and a sandwich sells for $6. If your uncle is maximizing his profit, what is the value of the marginal product of the last worker he hired? What is that worker’s marginal product?Coldbox Corporation hires its workers in a perfectly competitive labor market and produces and sells frozen peas in a perfectly competitive product market. The market price for frozen peas is $4 per bag. The table below shows Coldbox' short-run production of frozen peas. Labor is the only variable input. Coldbox Corporation's fixed cost is $500. Number of Workers Bags of frozen peas 0 0 1 60 2 140 3 250 4 320 5 380 6 400 a) If the wage is $200 per worker, identify the profit-maximizing number of workers for Coldbox. Explain using marginal analysis. b) If the price of frozen peas decreases by $2 per bag, would the number of workers hired by Coldbox be more than, less than, or equal to the number of workers you identified in part (a) ? Explain. c) Suppose that Coldbox hires workers from a monopsonistic labor market. Would the wage be higher, lower, or equal to the equilibrium wage in a perfectly competitive market? Explain.The production function of Amazon burgers, producers of delicious burgers is given as Q =6L -0.4L². The unit price of burger is $10 and it costs Amazon $20 to employ a unit labor Required How many units of labor should the firm employ to maximize profit if the firm is operating in the short run? Estimate the firm’s profit
- A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $12 per hour and capital is rented at $8 per hour. If the marginal product of labor is 60 units of output per hour and the marginal product of capital is 45 units of output per hour, is the firm using the cost-minimizing combination of labor and capital? If not, should the firm increase or decrease the amount of capital used in its production process?The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) ina very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital isrented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production isGH¢1,000. Suppose the firm’s production function (Q) is as follows:? = 14?0.5?0.5 + 10Determine the optimal input usage and the maximum profit.Suppose a short-run production function is described as Q=30L-0.05L^2 where L is the number of Labors used each hour. If each unit of output (Q) has a marginal revenue (price) of $5 and the marginal cost of labor is $40 per labor unit (L), how many units of labor (L) should be hired to maximize profit?
- 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?To maximize profit, a price taker will expand its output as long as the sale of additional units adds more to revenues (marginal revenues) than to costs (marginal costs). Therefore, the profit-maximizing price taker will produce the output level at which marginal revenue (and price) equals marginal cost. In a price-taker market, if a business produces efficiently (i.e., that is, where marginal revenues = marginal costs), the firm will be able to make at least a normal profit. True of False. ExplainA firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L1/2M1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)