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prove that dMRTS/dL<0 when FKL > 0
where MRTS =MPL/MPK
MPL= marginal product of labor
MPK - marginal product of capital
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Solved in 3 steps
- What shapes would you generally expect a total product curve and a marginal product curve to have?In the production process, both the average product and marginal product of the variable input rise first, then fall, and then rise to infinity OFalse O True 27 WSuppose we have a produ ction function for wheat Q = KL - 0.8K2 - 0.212 A. Given K = 10 Units, calculate the level of labourth at the AP reaches max andh ow Much wheatis produced at that point B. Given K = 10 at what level of labour outputreaches maximum C. How mu ch Ilevel of labor should the company hire in order to be efficient |
- 5. Cost Minimization Suppose a firm has the technology of F(K.L) 40LK Draw a graph of the firm's not at 8000 units of output (does not have to be exact). Put laboren the s-axis and capital on the y AXI What is the formals for the firm's MRTS at any level of Land K Suppose the price of labor is 5 while the price of capital is 10, and the fiem wants to produce 8000 units of output. What is the cost minimiring combination of labor and capital?1. Optimal Use of a Single Input. Julian Smyth manages production at Taffy Apple Inc., a company that produces a variety of taffy/fruit candies. Over the last several months, he has varied the number of employees on his caramel apple production line from 5 to 12, and found the following relationship. Labor S67∞a 5 8 9 10 11 12 TP 50 90 150 200 240 270 290 300 MP VMP a. In the column labeled MP, calculate the marginal product of labor. b. Suppose the apples sell for $6 per (dozen) box. Calculate the Value Marginal Product (VMP) c. If labor costs $200 per day, how many laborers should the firm hire? NumberA firm is currently producing such that: MPL = 30 W = 10 MPK = 20 To minimize the cost of production, this firm should: a. Use more labor and less capital which will (likely) decrease the MPL b. Use more labor and less capital which will (likely) increase the MPL C. Use less labor and more capital which will (likely) decrease the MPK Od. Use less labor and more capital which will (likely) increase the MPK v = 20
- ... Assume that the price of a car wawsh is $10 and the marginal product of labor at the car wash is given in the following table: Quantity of labor L (workers) 0 1 2 3 4 5 6 7 Quantity of car washes Q 0 6 11 15 18 20 21 21 Marginal Product of Labor (change in Q/change in L) aka car washes per worker • Fill in the values for MPL in the table • Calculate the MRPL for each quantity of labor • Draw a correctly labeled graph of the MRP curveGopher Excavators produces shovels in a small factory and sells the shovels in a competitive market. The following table shows the company's production function: Labor Output (Number of workers) (Shovels) 1 80 2 150 3 210 4 250 5 270 Use the blue points (circle symbol) to plot the production function for Gopher Excavators on the following graph. 300 270 240 Production Function 210 180 150 120 90 60 30 LABOR (Number of workers) OUTPUT (Shovels)MCQ 45 Suppose the production function exhibits constant returns to scale, with diminishing marginal productivities for both capital and labour. For this function, we would expect a fall in employment and an increase in the capital stock to generate: A a fall in the marginal product of labour and a fall in the marginal product of capital I do not want to answer this question. a fall in the marginal product of labour, but the change in the marginal product of capital can't be determined from the information provided D a rise in the marginal product of labour and a fall in the marginal product of capital E a rise in the marginal product of labour and a rise in the marginal product of capital F a fall in the marginal product of labour and a rise in the marginal product of capital
- i Saved Help Save & Exit Sul Instructions: In parts a and b, enter your responses as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. a. Calculate marginal physical product (MPP). Labor Output(Q) MPP 0 0 10 2 22 3 30 36 5 38 6 37 b. When does marginal productivity first diminish? When worker is hired.Define marginal product of labor and value of the marginal product oflabor. • Describe how a competitive, profit-maximizing firm decides how many workersto hire.OFair,%20Sharon%20E.%200ster%20-%20Principles%20of%20Econo.. Page view AN Read aloud I Draw E Highlight Erase 2.6 The following table represents data for Sally's Salon. Draw a graph showing the total product, marginal prod- uct of labor, and average product of labor. Identify where increasing returns, diminishing returns, and negative returns set in on the total product curve. Labor Units Total Product (Haircuts Per Day) Marginal Product of Labor Average Product (Employees) of Labor 7. 7.00 17 10 8.50 3 31 14 10.33 4 44 13 11.00 55 11 11.00 64 9. 10.67 69 9.86 69 8.63 9. 65 -D4 7.22 10 59 5.90 2.7 Assume that we have a production process that exhibits increasing and then decreasing marginal productivity. That is, as we increase output, the marginal product of labor starts at some level above zero, rises to a maximum, and then eventually falls to zero. Which of the following statements is truc? Briefly explain 6:07 PM Desktop d) ENG 4/23/2021