Consider the following Cob-Douglas production function: f(k.1) = K°P°, where a 20 and > 0. 1. Show that the production function is homogeneous of degree n in inputs. What does n equal? 2. Using your answer from part (1), if a + 3 < 1, is the Cobb-Douglas production constant returns to scale, increasing returns to scale, or decreasing returns to scale? What if a+8 = 1? What if a+8 > 1? 3. Now suppose that a = 1/3 and = 1/3. What is the firm's marginal product of labor (MP)? What happens to the MP, when the firm's use of labor increases? Are labor and capital Edgeworth complements or substitutes?
Q: Assume a Cobb-Douglas production function of the form: q = 10L0.24 K0.51 What type of returns to…
A: Return to scale define the level of production in the firm , so here we calculate the return to…
Q: Under what conditions do the following production functions exhibit decreasing, constant, or…
A: In a market, the production function represents the nature of the input resources in terms of their…
Q: Consider the following equation: Y = F (K, AN) Based on this equation, explain the concepts of…
A: Given, Y=F(K, AN)where, Y is output K is Capital and AN is Effective Labor.Here, Y is a function of…
Q: With the Cobb-Douglas production function Y=zK1/4nd374, if both capital and labour increase by 20%,…
A: Answer: Given, Production function: Y=zK14Nd34 Increase in both capital and labor = 20% Value of K…
Q: The production function of a firm is x= A* l^a* k^(1-a-b)*e^b. l is labor, k is capital, e is…
A: Hello. Since you have posted multiple parts of the question and not specified which part needs to be…
Q: H8. Which of the following production functions exhibit(s) constant returns to scale?I. Q = Min…
A: There are CRS if the doubling the all inputs result in the double of output.
Q: Suppose that firms face the following production function: Q = 10 + L+K+2L/2K1/2, This production…
A: please find the answer below.
Q: Determine the returns to scale implied by each of the production function. Q = 0.4Y1/2 +…
A: Q (Y,A,B) = 0.4Y1/2 + 0.3A1/4B1/4 + 2.0B1/2 To determine the returns to scale, we will multiply Y,…
Q: If a firm has a constant returns to scale production function F(K,L), then the ratio of inputs K L…
A: In long run firm experiences return to scale on its production function which are 1.Constant return…
Q: onsider the following production function: Q = 2K + 6L where K represents Capital, L represents…
A: Production function shows the different combinations of inputs that a firm uses in order to produce…
Q: Which of the following production functions exhibits decreasing returns to scale? A) Q=K^1/2 L^1/2…
A: Returns to scale are used to describe how production scale changes when all the factors of…
Q: A firm with decreasing returns to scale can expect to produce [a. more than, b. less than,…
A: Returns to scale Returns to scale is a metric for determining how efficient a production function is…
Q: increasing, decreasing
A: A production function tends to relate the physical output of a production process to factors of…
Q: Assuming that the production function [Y=A(K, L, N, H)] exhibits constant returns to scale we can…
A: In economics, the term "returns to scale" basically refers to the variation or change in…
Q: Assuming a Cobb-Douglas production function with constant returns to scale then, as K rises with L…
A: Cobb-Douglas is a specific functional form of the production function, generally used to represent…
Q: Explain the three types of returns to scale with Cobb-Douglas production function.
A:
Q: Given that the production function Q=L^0.75 K^0.25, describe the type of returns to scale exhibited…
A: Given: Q=L0.75K0.25
Q: Consider the production of some output Q using capital K and labour L. a) Assume K is fixed. Draw a…
A: Production function refers to that function which provided maximum level of output for given level…
Q: Show whether the following production functions exhibit decreasing returns to scale (DRS), constant…
A: Production function shows the output produced in an economy by using the available factors of…
Q: Margeʹs Hair Salon production function is Q = f(K, L) = K0.5L0.5 where K is the number of hair…
A: 2.1 Prove, with the aid of mathematics, the type of returns to scale exhibited by this production…
Q: For a linear production function what is the short-un production function given that capital is…
A: Given information: q=f(L,K) = 10L + 4K Where q is the quantity produced; L is labor; K is capital…
Q: Answer all the following seven parts. (a) Show the conditions for a Cobb-Douglas production function…
A: The term "long-run" refers to a period during which the production function is determined solely by…
Q: 3.1 Consider the following production function: F(K,L) = K®.3L0.7 State if this function exhibits…
A: disclaimer :- as you posted multipart questions we are supposed to solve the first 3 questions only…
Q: Determine the returns to scale of this production function: F (x1, x2) = [xỉ + x]\/2 A. Constant…
A: If change in inputs changes output by an equal proportion, production function has constant returns…
Q: (1) f(L, K) = ALªK!-a (2) f(L, K) = (min {iL, jK})²
A: Returns to scale refers to how much output changes given a proportional change in all inputs- where…
Q: Suppose a producer faces the following production function: K^0,5.K^0,5 given that L is the unit of…
A: The total cost refers to the expenditure incurred by the producer in producing all units of goods or…
Q: Optimize the Cobb-Douglas production function given the following parameters. The maximum about of…
A: (Q) Optimize the Cobb-Douglas production function given the following parameters. The maximum about…
Q: hen a production function exhibits constant returns to scale, it means that: A. a proportional…
A: Constant returns to scale production function means that the production function is…
Q: y = F(L,K) = min(L,3K) Show if the leontie
A: Here, we have to find constant returns to scale.
Q: Consider several production functions below and indicate whether they exhibit constant, increasing…
A: The markets are the place where the buyers of various goods and services tend to interact and meet…
Q: Which of the following production functions do not exhibit constant returns to scale? A. F(K, L)= AK…
A: Introduction Returns to scale refers to the how much output changes given a proportional change in…
Q: The Cobb-Douglas production function for a company building widgets is given by Y = AL K*- where Y…
A: Given: β = 0.81Y = ALβK1-β
Q: Which of the following production functions exhibits constant return to scale?
A: The production function exhibits constant returns to scale when there is a proportionate change in…
Q: For the production function Q = 0.2L2 returns to scale is: a.Constant Returns to Scale…
A: Returns to scale exhibits what happen to scale of production in long run when its factor of…
Q: How would you determine that a two-input Cobb-Douglas production function has decreasing returns to…
A: Answer to the question is as follows :
Q: You are given the production function: Q(K,L)=10KαLβ Does the above function exhibit increasing,…
A: The since long run alludes to a time-frame where the production function is characterized based on…
Q: The production function q = 9K0.8L0.1 exhibits: a. increasing retruns to scale b. constant…
A: The relationship between ou>tput and proportional increase in all the inputs is referred to as…
Q: Show that the following production function has constant returns to scale. It can be through a…
A: Given Production function y=5x11/2x21/2 We have to show that production function has constant…
Q: If the production function is Q = K5L.5 and capital is fixed at 1 unit, then the average product of…
A: Economics is a branch of social science that describes and analyzes the behaviors and decisions…
Q: How would you determine that a two-input Cobb-Douglas production function has decreasing returns to…
A: Answer to the question is as follows :
Q: A firm’s production function is - y = f(X1, X2)= X11/2 + X1X2 , Where X1≥0, X2≥0 1. Find its…
A: The returns of scale are of three types 1. Increasing returns of scale 2. Constant returns of scale…
Q: For the production function q = f(K, L) the ratio of the percentage change on with PK is called…
A: cobb douglas production function:- Q=ALαKβ in the cobb douglas production function, we have…
Q: The production function of a firm is x= A* l^a* k^(1-a-b)*e^b. l is labor, k is capital, e is…
A: Maximizing the profit function with respect to l, k and e above and setting it to zero we will get…
Q: Assume labor (L) is the only variable input used in the production process, a firm’s production…
A: Production refers to the process in which the output is produced using the factors of productions.…
Q: Determine whether each of the production functions below displays constant, increasing, or…
A: Answer in step 2.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
- You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled 1.Find the ranges of the three stages of production. 2.Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above 3.At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? 4.Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled a. Find the ranges of the three stages of production. b. Demonstrate the relationship between Total Production, Marginal Product and Average Product in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above c. At the end of the year it is expected that output will double with purchase of new equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadar plant…Suppose a soap-manufacturing production process is described by the following equation: Y = a + b log K + с log L Where, Y= Output (number of soaps produced) K=Capital L=Labor a, b and c are constants Suppose 0<a<1, 0< b<1 a. Find the Marginal Product of Labor (MPL) and Marginal Product of Capital (MPK) in the production of soap b. Is MPL diminishing, increasing or constant as L increases? c. Is MPK diminishing, increasing or constant as K increases?
- If the form of the production function is a Cobb-Douglas function, do diminishing marginal products apply here?Consider the following production function: f (A, B) = gamma multiply A^alpha multiply B^Beta. where A and B are the inputs and alpha, Beta, gamma are in the set (0,1). Let wA and wB the price of the two inputs. Assume wA, wB > 0. Is the production function separable?Does the production function exhibit constant returns of scale?Compute the cost function and the conditional input demand function.How do these three functions react to a change in wA? Suppose the price of both inputs double, what happens to the conditional input demand function? And to the cost function? Suppose the desired level of output double, what happens to the conditional input demand function? And to the cost function?…Qno1. You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Required. a) .Find the ranges of the three stages of production. b) .Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above . c). At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital.Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2,do you observe increasing, decreasing or constant returns to scale? d). Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…
- Production is described by the function f(K, L) = AL0.3K 0.3, A > 0.a. Interpret the exponents of the function f( K, L) and the parameter A. b. Explore the effects of scale of this production function. Does the answer depend on A?c. What is the degree of homogeneity of this function? Does the answer depend on A? d. Consider a production function given by F(K, L) = f 2(K, L ). How do the answers to thequestions in b. and c. change?e. Consider a production function given by F(K ,L) = f(K, L) + 2. How do the answers to thequestions in b. and c. changeFor the Cobb-Douglas production function P and isocost line (budget constraint, in dollars), find the amounts of labor L and capital K that maximize production, and also find the maximum production. Then evaluate and give an interpretation for |å| and use it to answer the question. (a) Maximize P = 2000L3/5K2/5 with budget constraint 15L + 32OK = 8000. L = K = P = (b) Evaluate and give an interpretation for |21. Each additional dollar of budget increases production by this amount. (c) Approximate the increase in production if the budget is increased by $80. unitsConsider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True False
- You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Find the ranges of the three stages of production. Demonstrate the relationship between Total Production, Marginal Product and Average Product in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively…Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an expression for the marginal product of x1. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain What is the the technical rate of substitution between x2 and x1? What is the type of returns to scale of this production function? (Increasing, decreasing, constant)Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…