Consider a competitive firm in both input and output markets. The production function for this firm is given by q = 10 (KL)^.2. The price of K is $1 and the price of the output is $5. Derive the demand for labor when K is variable.
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Consider a competitive firm in both input and output markets. The production function for this firm is given by q = 10 (KL)^.2. The
Derive the demand for labor when K is variable.
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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?A manager hires labour 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, whereas the marginal product of labour is 60 units of output per hour and the marginal product of capital is 45 units of output per hour. Show if the firm is using the cost-minimizing combination of labour and capital and give appropriate advice if necessary.The production function of a competitive firm is described by the equation y = 1/2, 1/2 2.x26x. The factor prices are pi $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 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?Widget factory Inc. in Wisconsin has the following production function: F(L,K)=2L L represents the number of labours hours. Workers at this factory are paid an hourly wage of $30 and they rent capital at$25/ hour.since this is a competitive market, the factory output is $50 per unit. Let's pretend the firm operates in the short run with capital fixed at 900, how many workers would widget factory Inc employ? What is their profit rate?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.
- A firm pays a price w for each unit it employs of its labor x. It also incurs fixed costs equal to F. If the firm receives a price p for each unit of output produced, and it produces output given by f(x) = 4x¹/4, how much of labor x should it employ to maximize profits? Verify whether your answer is indeed a maximum.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?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.
- Suppose in a purely competitive product market, price is $10. If a firm's production function is given as Q = f(L,K) = L04K0.6. a) Calculate firm's labor demand curve. b) Calculate firm's capital demand curve.Suppose that a firm's only variable input is labor. The firm increases the number of employees from four to five, thereby causing the weekly output to rise by two units and total costs to increase from $3,000 per week to $3,300 per week. What is the marginal product of hiring five workers instead of four? What is the weekly wage rate earned by the fifth worker?The market for drones is perfectly competitive. Labor is the only variable input. The fixed cost is $500. Based on the information in the table below, what is the Marginal Product of Labour when Q=300? Enter a number only, drop the $ sign. Wage rate =$100 per unit of Labour Quantity Quantity of of Labour Output 8 44 15 213 21 300 43 433
