a. The production function represent the long run as both the inputs labour and capital are variables here, whereas in the short run, one of the inputs is fixed.
b. i. Average Product = Total product/Number of workers = 37/5 = 7.4
ii. Marginal product of 6th worker = Total product with 6 worker - Total product with 5 worker = 42 - 37 = 5
iii. Yes, production function eventually does exibit diminshing returns, it exibits diminishing returns after 5 workers, i.e while adding 6th worker. it happens so because the fixed capital of 3, is optimally utilized with 5 workers only, hence adding 6th worker reduces the marginal returns.
C. The shapes of two isoquants suggest that the marginal product of both the inputs is extectly same.
D. the production function exibits constant returns to scale CRTS as it can be seen from the table that when both the inputs are increased by same proportion output also increases in the fixed amount. As L and K increases from 1,1 to 2,2 then output increases from 5 to 15.
Answer the following questions based on the following production function: Does this production function represent the...
b. Does this production function have an uneconomic region? If yes, find the region. c. Based on your answer to (b), sketch a graph of two isoquants Q1 and Q2 withQ1 < Q2. 1. (12 points) Consider the production function Q = KL2-L", and answer the following questions. a. (4 pts) Does this production function exhibit diminishing marginal product of capital? Diminishing marginal product of labor? Explain.
A6 Microeconomics Assignment 6 Part I: Short Answer Questions [(100 points) Q1 [30 points) Show in a diagram using isoquants that a production function can have diminishing marginal return to a factor and constant returns to scale? With the help of a diagram explain the concepts of "isoquant", "diminishing marginal return to a factor", and "constant returns to scale". What are the similarities and differences between indifference curves and isoquants. Q2 [30 points Assume that a firm has a fixed-proportions...
The following table shows a short-run production function for yoga pants. Use the data to determine where diminishing targinal product begins. Number of workers Total output of yoga pants 120 325 Diminishing marginal product begins when the company hires worker number
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
Complete the following table for the following production function 8) The production function and the diminishing average product of labor a) Complete the following table for the following production function (round off to nearest whole number): | | Average product of labor (kg/worker) # of workers 10 20 30 40 50 60 70 80 Grain output (kg) 632 894 1,095 1,265 1,414 1,549 1,673 1,789 b) Given the above data graph the production function. Show how to represent the average...
3) Consider the production function ? = 6? 0.3? 0.6 . The marginal products are ??? = 1.8? −0.7? 0.6 and ??? = 3.6? 0.3? −0.4 . a. In the short run assume that capital is fixed at ? = 10. Derive formulas for the short-run Total Product (TP), Average Product (APL), and Marginal Product (MPL). Graph these three functions. b. In the long run, capital is not fixed. Graph the isoquant for ? = 6. Identify and label three...
The following table shows a short-run production function for tablets. Use the data to determine where diminishing marginal product begins. Number of workers Total output of tablets 0 0 1 50 2 120 3 180 4 230 5 280 6 325 7 320 8 310 Diminishing marginal product begins when the company hires worker number
Consider a firm that has the following CES production function: Q = f(L,K) = [aL^ρ + bK^ρ]^1/ρ where ρ ≤ 1. Please clearly show each STEP and make sure your handwriting is LEGABLE. Thank you Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) What are the returns to scale for this production function? Show...
Q1 [30 points] Show in a diagram using isoquants that a production function can have diminishing marginal return to a factor and constant returns to scale? With the help of a diagram explain the concepts of "isoquant", "diminishing marginal return to a factor", and "constant returns to scale". What are the similarities and differences between indifference curves and isoquants. Q2 [30 points Assume that a firm has a fixed-proportions production function, in which one unit of output is produced using...
8) The production function and the diminishing average product of labor a) Complete the following table for the following production function (round off to nearest whole number): # of workers 10 20 30 40 50 60 70 80 Grain output (kg) 632 894 1,095 1,265 1,414 1,549 1,673 1,789 Average product of labor (kg/worker) b) Given the above data graph the production function. Show how to represent the average product of labor on your graph. e) Explain what diminishing average...