Consider the following production functions, where q is the quantity produced of the good, Kis the quantity of capital used, and L is the quantity of labor used:Production function 1: q (K, L) = KªLBProduction function 2: q (K, L) = K² + L1. Suppose that a = 1 and ẞ= 1. Does Production function 1 have decreasing, constant, orincreasing returns to scale? Explain.2. Suppose that a = 1 and ẞ= 1. Does Production function 2 have decreasing, constant, orincreasing returns to scale? Explain.3. Below is a Total Product table for production function 1 when a = 1 and ẞ = 1.KIL 1 2 3455112 345 162246 810 123369 12 15 18st4812 16 20 2455 10 15 20 25 306 612 18 24 30 36Suppose that the level of capital is fixed at 5 units. What is the marginal product of labor (MPL)for each unit of labor employed? Does the MP, vary with number of units of labor used?

To determine the returns to scale for a production function, we need to multiply the inputs by a…

Answered: Consider the following production…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.9P

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QUESTION 1 Consider the following production functions, where q is the quantity produced of the good, Kis the quantity of capital used, and L is the quantity of labor used:Production function 1q (K, L) = K^αL^βProduction function 2q (K, L) = K^α + L^βa) What is production function? Explain by providing appropriate graph.b) Does Production function 1 have decreasing, constant, or increasing returns to scale?Explain.c) Suppose that α = 1 and β = 1. Does Production function 2 have decreasing, constant,or increasing returns to scale? Explain.d) Suppose that α = 1/2 and β = 1/2. Does Production function 1 have decreasing,constant, or increasing returns to scale? Explain
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.
Consider the following production functions and match them to the word that describes their returns to scale. Production function A: F(L,K) = K²L Production function B: F(L,K) = 25K + 10L Production function C: F(L,K) = (KL)¹2 Production function D: F(L,K) = 5L² + L¹/2K1/2 Production Function A✔ Choose... Decreasing Production Function B Constant Production Function C Increasing Production Function D Choose.. +
Suppose that q = 40, L = 5, and K= 10 is a point on the production function q=f(L, K). Is it posssible for q = 40, L = 5, and K = 11 to also be a point on this production function? Why or why not? The combination q =40, L = 5, and K=11 A. cannot be a point because we assume production functions are comprised of fixed inputs. B. can be a point because we assume production functions hold technology constant. C. cannot be a point because we assume production functions are efficient. D. cannot be a point because we assume production functions represent the short run. E. can be a point because we assume production functions exhibit diminishing returns.
Give only typing answer with explanation and conclusion Consider a production function with two inputs: f(x1,x2) = (x1)a(x2)b Suppose that a = 0.7 and b = 0.7. What type of returns to scale does this production function exhibit? Type 1 for increasing, 0 for constant, and -1 for decreasing.
Which of the following production functions exhibit constant returns to scale? In each case y is output and K and L are inputs. (1) y = K 1/2 L 1/3 (2) y = 3 K 1/2 L 1/2 (3) y = K 1/2 + L 1/2 (4) y = 2 K + 3 L. O 1, 3, and 4 O 1, 2, and 4 2 and 4 2, 3, and 4 2 and 3
please answer the following, I have attached an image of the question for better format. Thanks! 2. Suppose that the production function of a country is given by Y=K3L0.7, where Y is output, L is labour, and K is capital. a)What is the return to scale property of the production function? B)What will happen to output if we double the use of capital and labour? C)Write the production function as a relationship between output per worker and capital per worker.
1. Assume that a firm has the following production function: q = L0.5K0.6 a. Calculate output when L = 64 K = 32. b. What returns to scale does this production function exhibit? c. Calculate output if technology utilized by the firm increases by 25%. d. Determine, both, the marginal product of labour and capital functions (ignore c.). e. Calculate, both, the marginal product of labour and capital when L = 64, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 64, K = 32 and interpret your answer.
3. Suppose that the production function is Q=L075K©25, a) What is the average product of labor holding capital K fixed. b) What is marginal product of labor? c) What is marginal product of capital? d) What is MRTS?
Given the production function y=(l^p + k ^1/p )^1/p , what is the technical of substitution, the elasticity of substitution, and the returns to scale when p = 0.5?
I need the answers of a,b,c
Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). From the graph we know that for the corresponding K: APL(L1,K)=MPL(L1,K) APL(L2,K)>MPL(L2,K)…

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