Production Function. Consider the Cobb-Douglas production function discussed in class: F(K, L) = AK1/3 L2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. D) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com- ment on how and why these numbers changed relative to (c) and why they did so.

Production Function. Consider the Cobb-Douglas production function discussed in class: F(K, L) = AK1/3 L2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. D) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com- ment on how and why these numbers changed relative to (c) and why they did so.

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter17: Economic Growth: Resources, Technology, Ideas And Institutions

Section17.2: A Production Function And Economic Growth

Problem 4ST

See similar textbooks

Similar questions

Let the production of Y use two factors K and L. The production function is given by: Y =√4?√9?. If the prices for capital and labor are the same, then show that the firm will use the same quantities of K and L.
Jolene has a production function 4?1 + ?2. If the factor prices are £12 for factor 1 and £2 for factor 2, how much will it cost her to produce 30 units of output? Use lagrange to solve this
1. Given the production function Q = f(L,K) = KL2 – L3 , where Q is output and L and K are the labor and capital inputs, respectively. Suppose K is a fixed input set at 15 units. Mathematically and graphically show the input levels that divide stages I & II and stages II & III of production.2.Consider the production functions for X and Y given below.X = 2K2 + 4L ; Y = 10K0.5 L0.5 ; Suppose the isocost equation is given by C = 4L + 10K, derive (i) the long-run cost function for good Y and (ii) the short-run cost function for good X if 10 units of capital are employed in X.3. Given: Q = 100K0.6L0.8; w = 50; r = 80; Q0 = 2,000. Graphically illustrate the expansion path for the firm if it decides to increase its target output to Q1 = 4,000.
Suppose that a certain factory output is given by the Cobb-Douglas production function ?(?, ?) = 60?^1/3?^2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory’s output. (a) Determine whether the Cobb-Douglas production function is concave, convex, strictly concave, strictly convex or neither.
David Ricardo ([1817] 1965) modified Smith’s model by introducing diminishing returns to land cultivation. Diminishing returns implies that as you apply more of a variable input (labor) to a fixed input (land), the productivity of each additional worker will eventually decline as long as technology isfixed. He claimed that land was of variable quality and finite. Thus, as an economy grows, population grows relative to land, and the productivity of the labor on the land will decline. According to Ricardo, the only way stagnation could be averted, at least temporarily, would be through the trade and imports of cheap food or wage goods. The essential doctrines of John Stuart Mill (1848) differed little, if at all, from those of Ricardo. He, like Smith, believed in the doctrine of laissez-faire , but he also recognized the possibility of modifying the system. He displayed a leaning to the socialist ideal, growing closer as his life advanced. He believed that we should sacrifice economic…
Suppose that we have a linear production function Q = 10L + 2K. (Quantity = labor + capital) If the price of labor is $5 per unit and the price of capital services, r, is $2 per unit. Find the optimal input combination given that the firm wishes to produce 200 units of output.
Ab 11 Economics A production function is given by the equation Q = 48L^0.5*K^0.5. Where L is the number of labor units and K is the capital units. Find the marginal product of labor (QL) and the marginal product of capital (Qk) at L=9 and K=16.
Consider the production function Y = z * K^1/3 * N^1/3 * L^1/3 where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land. Question text If we double the technology factor, z, then output will double. Question 17Select one: True False Question text If we increase the population, and therefore the workforce, then if nothing else changes, the average product of labour must increase. Question 18Select one: True False Question text We would need to increase capital input by a factor of 8 to double output. Question 19Select one: True False Question text Increasing technology will increase labour productivity. Question 20Select one: True False
Assume that a competitive economy can be described by a constant returns to scale, Cobb–Douglas, pro- duction function. Suppose that in this economy all factors of production are fully employed. Holding other factors constant, including the quantity of capital and technology, carefully explain how a one-time, 10-percent decrease in the quantity of labor will change labor’s share of total income?
Given the production function y=(l^p+K^p)^1/p, what is the technical rate of substitution and the the returns to scale when p=0.5?
Suppose there are two primary factors of production, labour (L) and capital (K), and there are nosecondary factors of production. The production function for this economy is simply Y = cKL,where c is a constant and α= 0.5. Which of the following is true? 1.This economy exhibits constant marginal product of labour 2.This economy exhibits decreasing returns to scale 3.This economy exhibits constant marginal product of capital 4.This economy exhibits diminishing marginal product of labour
Q5. Jason is running a cleaning business, there are available labours (L) and machines (M) for Jason to use as inputs to produce cleaning service for his clients. a) Suppose Jason must use both labours and machines without any specific ratio to complete the service for his clients, please write down the general production function formula for Jason. hint: you could use any letter if you want] b) Under the function form of a), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) equals to 2, how do you interpret it? c) Assume Jason now can use only single input, either labour or machine to complete the service, please write down the general production function formula for Jason. hint: you could use any letter if you want] d) Under the function form of c), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) is always larger than the market price ratio between labour and machine (w/r), what should Jason do? why?