Suppose that at a wage rate of $10, a firm which is using its resources efficiently has a marginal rate of technical substitution of 4, and at a $12.50 wage rate the marginal product of capital is 5. Then if there is an increase to a $12.50 wage rate and the firm makes the necessary adjustments to continue efficient resource utilization the marginal product of labor must be 25." Is this statement is true or false? First indicate the correct response and then explain your answer.
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- A firm can manufacture a product according to the production function Q = 2(K)1/4 (L)3/4 where K represents capital equipment and L is labor. The company has already spent $10,000 on the 4 units capital. a. Please show the expression for the average product of labor, APL and the marginal product of labor, MPL. If workers at the firm are paid a competitive wage of $100 and the product is sold for $200 each, what is optimal level of labor usage and what is the maximum profit?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 = $19The following table shows different combinations of labor and capital that can produce 400 units of output. The 3rd and 4th columns give the marginal products of labor and capital at each input combination. Suppose the wage rate is w=$1 and the price of capital is r = $5, what is the optimal input combination that produces 400 units at lowest cost? Marginal Marginal Product of Product of Labor Capital Labor Capital 10 2 80 400 2 10 400 80 4 5 200 160 5 4 160 200 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a L=10, K=2 b L=2, K=10 C L=4, K=5 d L=5, K=4
- Suppose that labor is the only input used by aperfectly competitive firm. The firm’s productionfunction is as follows:Days of Labor Units of Output0 days 0 units1 72 133 194 255 286 297 29a. Calculate the marginal product of each additionalworker.b. Each unit of output sells for $10. Calculate thevalue of the marginal product of each worker.c. Compute the demand schedule showing thenumber of workers hired for all wages from zeroto $100 a day.d. Graph the firm’s labor-demand curve.e. What happens to this demand curve if the price ofoutput rises from $10 to $12 per unit?Eva runs a small bakery in the village of Roggerli. She is debating whether she should extend her hours of operation. Eva figures that her sales revenue will depend on the number of additional hours the bakery is open as shown in the table above. She would have to hire a worker for those hours at a wage rate of $12 per hour. Refer to Table 1-1. Using marginal analysis, how many hours should Eva extend her bakery's hours of operations? 2 hours 3 hours 4 hours 5 hoursSuppose that the production of a certain product only requires one input, labor, and that the additional production diminishes by half after the last input. On the other hand, the demand of the good can be described using the equation Q = 10000 – P/10. The total product of the second unit of labor is 3,000 unite. Finally, each additional worker requires P1,000,000. Given the following information, answer the following questions: What is the marginal revenue product of the third unit of labor? Answer: 500 How would you characterize the marginal revenue product of labor? How would you characterize the labor market that this firm faces?
- The marginal rate of technical substitution of L=2K means that the firm can substitute 2 units of capital for an additional 1 unit of labor in the market. True or false.38. For the production function y = 3x₁ + 4x2 , which of the two inputs is more productive when x₁ is 1 and x₂ is 10 ? O. X1 O. X2 O. neither ; for this situation , they have equal marginal products O. cannot tell from the above information 39. Given the production function y = 3x₁ + 4x2 , what is the marginal rate of technical substitution of x₁ for x₂ ( MRSx1x2 ) when x₁ is 5 and x₂ is 5 ? O. -0.75 O. -x1 / 5 O. 5 O. -5Suppose Die Cast Aluminum Co. is a subcontractor for the auto industry and makes specialized auto parts. There is a bracket it manufactures that it sells for $2.50. The following table shows the number of brackets that can be produced from a given number of labor hours. Assume that the company cannot hire labor for a fraction of an hour. Hours of Labor Output 50 90 1 3 120 4 140 150 155 6 157 The marginal product of labor for the third hour of labor is 30. (Enter your response as an integer.) The value of the marginal product of labor for the third hour of labor is 75. (Round your response to two decimal places.) If the wage paid to workers in Die Casť's plant is $25/hour, it should employ worker(s). (Enter your response as an integer.) If the wage paid to workers in Die Cast's plant is $35/hour, it should employ worker(s). (Enter your response as an integer.) If the wage is $25/hour, but the price of a bracket declines to $2.00, it should employ worker(s). (Enter your response as an…
- Consider a firm that produces output using a typical production function as discussed in the course, and that hires workers in a competitive labor market. 1. Explain what determines the firm's choice of its labor input. Use a suitable figure. Discuss how changes in the capital stock and in the wage affect the firm's choice of its labor input. Suppose that the firm uses a Cobb-Douglas production function Y = K"N-«. In this case, the marginal product of labor is given by (1 – a)K“N-«. The parameter a is 2/3, and the firm uses one unit of capital. 2. Calculate (show your steps) how the firm's labor input changes if the wage increases by 1%. 3. Calculate how the firm's labor input changes if the wage is unchanged, but the firm decides to double its capital stock.Consider the Labor Economics Question. This will provide insight into the idea of the optimal number of workers and the value of the marginal product of labor. If wages in the restaurant is $16.80 per hour and the price of a Hamburger is $8.30 and the production function for the workers is: Q = 11L – 0.25L2 How many workers should Your Restaurant employ during the lunch hour to maximize profits? 1 Point (note—the value of the marginal product of labor and the marginal revenue product are the same) We maximize profits which are total revenues less total costs:Q40 If one worker in southern Ontario worker can pick $30 worth of tomatoes two workers together can pick $70 worth of tomatoes, the Multiple Choice data given are insufficient to determine the marginal revenue product of either worker. data given suggests diminishing returns. marginal revenue product of the first worker is $40. marginal revenue product of each worker is $35. marginal revenue product of the second worker is $40.