3. Frisbees are produced according to the production function q = 2K+L where q=output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant defined in part a and part b. What is the RTS along this isoquant? Explain why the RTS is the same at every point on the isoquant. d) Graph the q = 50 and q = 200 isoquants for this production function also. Describe the shape of the entire isoquant map. e) Suppose technical progress resulted in the production function for

3. Frisbees are produced according to the production function q = 2K+L where q=output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant defined in part a and part b. What is the RTS along this isoquant? Explain why the RTS is the same at every point on the isoquant. d) Graph the q = 50 and q = 200 isoquants for this production function also. Describe the shape of the entire isoquant map. e) Suppose technical progress resulted in the production function for

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

complete the table
Suppose that corns are produced according to the production function q = 100K + 50L, where q represents pounds of corns produced per hour, K is the number of acres of land devoted to corn production, and L represents the number of workers hired each hour. 1. Does this production function exhibit increasing, constant, or decreasing returns to scale? 2. Give one reason why this production function is probably not a very reasonable one.
2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 3 15 K=2 10 K=3 16 K=4 20 25 28 30 31 (i) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L? 8 15 21 12 19 25 22 28 17 24 30
2. Which of the following production functions with inputs K, L, and H exhibits Constant Returns to Scale (CRS)? (Assume Ā > 0 is a constant) a) Y = AK/2L/2 b) Y = ĀK/2L/3H/4 c) Y = ĀK/2 – L/H d) Y = ĀKL/2H\/2
If a firm has 5 units of capital, 10 units of labor, and the production function is Q = 4L + 3K what is the Marginal product of capital? 3 4 11 45
6
2. Consider a production function: x(l, k) = Alªk³. Showing all of your work: (a) Under what conditions are the marginal products of labor 1 and capital k positive? (b) Under what conditions are the returns to labor and capital diminishing? (c) Under what conditions are the returns to scale increasing, decreasing, and constant?
10. Do the following production functions have increasing, decreasing, or constant returns to scale? Show work.(i) Q = 3K+2L (ii) Q = 6KL
1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 3 8 12 15 17 K=2 10 15 19 22 24 K=3 16 21 25 28 30 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L?
Consider the following production function: Q = 100L0.5K0.5 Subject to the budget constraint 5L + 10K = 75; where L is labour and K is capital. If the optimal quantities of labour and capital were employed, then the total output is approximately: a. 530 units b. 1371 units c. 2150 units d. 604 units