Item 9 The following graph shows the marginal and average product curves for labor, the firm's only variable input. The monthly wage for labor is $2,000. Fixed cost is $120,000. APMP
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- A baker uses labor (L) and raw materials (M) to produce mini Muhlenberg Mule sugar figurines (q). The process is fairly simple as workers only must make the sugar mixture and pour the mixture into the mule molds. The baker’s production function is as follows f(L, M) = L 0.50M. Let wL and wM denote the prices of a unit of L and M, respectively. (a) Write the firm’s cost minimization problem if it wants to produce q units of output. (b) Write the Lagrangian function that describes the cost minimization problem. (c) Derive the long run conditional factor input demands for L and M as a function of wL, wM, and q; L ∗ (wL, wM, q) and M∗ (wL, wM, q). (d) Suppose wL = $25 and wM = $2. Determine the cost-minimizing combination of inputs if the baker wants to produce 200 mules. (e) Using wL = $25 and wM = $2 and the demand functions from part (c), write the firm’s long run cost function CLR(q).In the short run, a tool manufacturer has a fixed amount of capital. Labor is a variable input. The cost and output structure that the firm faces is depicted in the table below. Assume the product price is $4. Calculate the marginal revenue product and the marginal resource cost, and then complete the table. Instructions: Enter your answers as whole numbers. Quantity of Labor Marginal Product Marginal Revenue Hourly Wage Rate ($) Marginal Resource Total Product Total Labor Product ($) Cost ($) (Labor) Cost ($) 10 400 5 50 es 11 420 20 8. 88 12 438 18 11 132 13 454 16 14 182 14 468 14 17 238 15 480 12 20 300 The equilibrium wage rate ($) = The equilibrium level of labor use = workersGraph the isoquant below and explain Labor (x) 50 38 28 20 14 10 8 7 Capital (y) 3 6 9 12 15 18 21 24
- Using the table below, what is the Marginal Product of Labor for the 4th worker? Quantity produced Fixed Cost Variable Cost 6,000 6,000 6,000 6,000 6,000 6,000 6,000 Number of workers 500 1,000 1,500 2,000 2,500 3,000 1 1,000 1,900 2,700 3,400 4,000 3 4 6. 4,500 800 700 600 O 500GM cuts jobs at its Australian manufacturing unit GM will cut 500 jobs, or about 12% of its workforce, at its Australian plant because of a sharp fall in demand for its locally-made "Cruze" small car. Source: The Wall Street Journal, April 8, 2013 As GM cuts its workforce, how will the marginal product and average product of a worker change in the short run? Suppose that before the cuts the marginal product of GM workers is below their average product. As the number of workers decreases, the marginal product of a GM worker and the average product of a GM worker in the short run. increases; decreases does not change; does not change decreases; decreases increases; increases decreases; increasesAssuming the firm is minimizing its cost and the price of labour is $10 per unit and the price of capital is $20 per unit. the marginal product of labour is 50, what must the marginal product of capital be?
- Consider the following diagram showing a range of isoquants and isocosts, with labour measured on the horizontal axis and capital measured on the vertical axis. Assume that when the firm is producing in the short run, capital is fixed at K but capital is variable in the long run. K, Capital K A B Q3 Isoquant Q2 Isoquant Q₁ Isoquant L, Labour Which of the following can we conclude? O Only point B represents cost minimisation in both the short run and the long run, as it is on the short run expansion path, as well being the cost minimising point in the long run. Points A, B and C represent cost minimisation in the long run only. There are no points that represent cost minimisation in both the short run and the long run. Points A, B and C represent cost minimisation in both the short run and the long run. Points D and E represent cost minimisation in the short run only. Points A, B and C represent cost minimisation but only in the short run. Points D and E represent cost minimisation in…A small specialty cookie company, whose only variable input is labor, finds that the average worker can produce 100 cookies per day, the cost of the average worker is $32 per day, and the price of a cookie is $1.00. Is the firm maximizing profit? The firm A. is not maximizing profit because the marginal revenue product of labor is greater than the wage. B. is not maximizing profit because the marginal revenue product of labor is less than the wage. C. is maximizing profit because the marginal product of labor is greater than the wage. D. is not maximizing profit because the price of the output is not equal to the wage. E. is not maximizing profit because the marginal product of labor is greater than the wage.The table below shows ABC firm short-run production function. The company hires workers at a wage rate of $400 a day and his total fixed cost is $1000. Labor (workers) Total product (output) 0 0 1 12 2 25 3 30 4 44 5 50 Calculate the average total cost of producing 25 Calculate total cost of producing 47 units. Calculate average variable cost if 30 units are produced. Calculate the marginal product of producing 44 units. Calculate average product of the 4th worker
- Macmillan Learning Consider the table, which reports production information for a firm that uses a fixed amount of capital and varying amounts of labor. Use this information to answer the questions. Do not round answers. What is the marginal product of the third worker? Third worker's marginal product: units What is the average product of the second worker? Round your answer to the nearest whole number. Second worker's average product: units What are diminishing marginal returns, and with which worker do they set in for this firm? Diminishing marginal returns occur in the short run when variable inputs are added to a fixed input, and marginal product declines. In this case, diminishing returns set in with the fourth worker. O Diminishing marginal returns occur in the short run when variable inputs are added to a fixed input, and product declines. In this case diminishing Workers 1 2 3 4 Output (total product) 23 27 33 37Consider the following short run production information: Units of Total Marginal Product Average Product Labor Product of Labor of Labor 4 16 5 6. 120 30 The marginal product of the 5th unit of labor is equal to 36 O Insufficient information 26 28Suppose that a firm has only one variable input, labor, and firm output is zero when labor is zero. When the firm hires 5 workers the firm produces 85 units of output. Fixed costs of production are $5 and the variable cost per unit of labor is $10. The marginal product of the sixth unit of labor is 4. Given this information, when the firm hires 6 workers the total output is amount to $ variable costs are $ production (rounded to the nearest cent) is cents. units, the fixed costs and the average total cost of