N6 Consider the following production function:q = f(K, N) = 4KN,where q is output, the two inputs are capital K and labor N.For this production function, what is the marginal product of labor (MPN)?part 1O MPN = 4O MPN = 4NO MPN = 4/NMPN = 4K/NO MPN = 4KFor this production function, which of the following statements is true?part 2Capital and labor are substitutes.There is diminishing marginal product of labor.There is diminishing marginal product of capital.Capital and labor are complements.O None of the above.

Answered: Consider the following production…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.3P

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1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.
2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function Y = K2/6 L3/6 H1/6 a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is found by differentiating the production function (Y) with respect to labor (L)) b) Derive an expression for the marginal product of capital. How does an increase in the amount of human capital affect the marginal product of capital? (Hint: The marginal product of capital MPK is found by differentiating the production function (Y) with respect to capital (K)).
X 15:01 EC5011 - Seminar 2.do... II. Problems and Exercises .ıl 4 1. Consider the following production function: . Does this production function exhibit constant returns to scale? (Hint: Replace K and L by 2K and 2L, respectively, and check if F(2K, 2L) = 2F(K, L).) 2. Consider the following production function: . a. Calculate the marginal product of labour. b. Calculate the marginal product of capital. c. Does this production function exhibit diminish MPL and MPK? d. Does this function exhibit constant returns to scale? 3. Suppose represents the production function of both Mexico and Spain. Use the following information to answer the next questions. L = Population K = Capital Y = Output Country (millions) (trillion) (trillion) Mexico 105 0.18 1.0 Spain 45 0.74 1.7 a. Calculate total factor productivity for both countries using the PF in question 2. b. Calculate per capita income for both countries. c. Explain the difference in per capita income. 4. A snack food factory in the Tuas…
Henry owns a Boba tea shop and produces delicious drinks under the production function q = 5KL where q is the number of servings generated per hour, K is the number of tea pots (capital), and L is the number of employees hired per hour (labor). The average product of labor and the marginal product of labor are both equal to APL = MPL 5K. Does labor exhibit diminishing marginal returns in this case? O No, the marginal product of labor is constant (for a given K). O No, the marginal product of labor is increasing (for a given K). O Yes, if capital also exhibits diminishing marginal returns. O Yes, this is true for all values of K.
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se The marginal product of labor can be determined using the total product of labor Production Function curve. 3,500- se Using the equation for the production function, 3,000- 3 2 q= 8LK + 5L2 – 2,500- see the level of output when L= 5 and K= 25 is (Enter a numeric response using 2,000- a real number rounded to two decimal places). 3 1,500- When labor is 5 units and K is 25, the marginal product of labor is 1 1,000 *** When labor increases to 12 units and K is 25, the marginal product of labor is 500 - 12 10 15 Labor Input (L) 15 20 25 DEC 25 tv 20 MacBook Air DII SO F10 F11 F9 F3 F4 * %23 $ & 4 6 8 { } E Y U P D F G н J K > C V N M command option - - ... .- V Product or Output (g) B R
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In the short run, a firm cannot vary its capital, K=2, but it can vary its labor, L. It produces output, q. You are given two production functions. (a) q = 10L + K MPL = 10 (b) q = L0.5K0.5 For each production function, please determine whether the production function will show diminishing marginal product (diminishing marginal returns) as labor increases. You must give an explanation for each answer. (Note: Diminishing returns of labor refer to the decrease in marginal product of labor as the quantity of labor increases).
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Consider the following production function: q = f(K, N) = 4KN, where q is output, the two inputs are capital K and labor N. For this production function, what is the marginal product of labor (MPN)? part 1