dont copy from chegg please Consider a firm that produces output using a typical production function as discussed in thecourse, and that hires workers in a competitive labor market.1. Explain what determines the firm's choice of its labor input. Use a suitable figure.Discuss how changes in the capital stock and in the wage affect the firm's choice of itslabor input.Suppose that the firm uses a Cobb-Douglas production function Y = K"N1-a.In this case, the marginal product of labor is given by (1– a)K"N-".The parameter a is 2/3, and the firm uses one unit of capital.2. Calculate (show your steps) how the firm's labor input changes if the wage increases by1%.3. Calculate how the firm's labor input changes if the wage is unchanged, but the firmdecides to double its capital stock.

A firms optimal level of input choices are achieved at the point where the value of marginal product…

Answered: onsider a firm that produces output…

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter18: The Markets For The Factor Of Production

Section: Chapter Questions

Problem 3PA

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Suppose that the production function is Yt = AtKt^(1/2) Lt^(1/2) where Yt is output, Kt is the stock of capital and Lt is amount of labor firms hire. Assume that Kt = 100, At = 2. (a) Firms in this economy maximize their profits, given by revenue net of labor costs: Yt −WtLt . Derive the firm’s labor demand curve. (b) Workers in this economy maximize their utility, given by U(Ct , Nt) = log(Ct) − Nt , where Ct is consumption and Nt is the amount of labor workers supply. Their budget constraint is Ct = WtNt . Derive the workers’ labor supply curve. (c) Calculate the equilibrium wage rate and employment in this economy using the expressions for labor demand and supply you derived above. Also calculate the total amount of output the economy produces. (d) Suppose that capital doubles, to Kt = 200. Calculate what happens to the wage rate, employment and output. Illustrate the effects of this increase in capital graphically, using a labor demand/supply diagram.
Consider a Cobb-Douglas production function:f(l, k) = Alα k1−α,where A is the total factor of productivity (a constant greater than 1), 0 < α < 1, lrepresentslabor, and k represents capital. The following sub-questions will guide you through showing thatthe elasticity of substitution is constant.a) Find the marginal product of labor. Verify that this production function exhibits diminishingmarginal productivity of labor. b) Find the marginal product of capital. Verify that this production function exhibits diminishingmarginal productivity of capital. c) Find the marginal rate of technical substitution. Write your answer as MRT S = . . . d) In part (C), you should’ve found the MRTS as a function of the input ratio, kl. Take theabsolute value of both sides and solve for the input ratio, so that the expression gives theinput ratio as a function of MRTS (i.e. kl = . . .). Take the log of both sides, then take thederivative with respect to the log of MRTS. Is the elasticity of…
Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r,respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of$1,500.a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in thelong run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph aspart a, graphically show the impact of the minimum wage on the optimal level of employment in thelong run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price ofcapital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts theoptimal levels of employment and capital in the long run. Clearly identify the resulting scale andsubstitution effects caused by the lower cost of capital. Could you please answer this question using the graphs please.
Use the table to answer the question that follows. Quantity of Labor MP of Labor Quantity of Capital MP of Capital 1 30 1 50 2 25 2 40 3 20 3 35 4 15 4 15 5 10 5 5 What combination of labor and capital would satisfy the input hiring rule that minimizes the cost of production, if the price of labor is $5 and the price of capital is $10? A-1 unit of labor; 3 units of capital. B-2 units of labor; 2 units of capital C-3 units of labor; 2 units of capital. D-4 units of labor; 4 units of capital E-5 units of labor; 1 unit of capital
Suppose, the demand and supply curve in a US manufacturing firm are provided as follows: ES = 20 + 2w ED = 70 − 3w where E is the level of employment and w is the hourly wage. Let’s assume this firm shows the representative wage of the manufacturing industry. Suppose the price of each unit of capital used in this industry is $25. The price of output is constant at $50 per unit. The production function is f(E,K) = E½K ½ , so that the marginal product of labor is MPE = (½)(K/E) ½ If the current capital stock is fixed at 1,600 units, how much labor should the industry employ in the short run? How much profit will the industry earn?
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.
During the 1920s, Charles Cobb and Paul Dougkas modeled totalproduction output P (of a firm, company or entire economy) as a function of labourhours involved x and capital invested y (each includes the monetary worth of allbuildings and equipment). The Cobb-Douglas production function isP(x, y) = k x^α y^(1−α),where k ad α are constants representative of a particular firm or economy.(1) Show that doubling of both labor and capital results in doubling productionP.(2) Suppose a particular firm has the production function for k = 120 andα =3/4. Assume each unit of labor costs $250 and each unit of capital costs$400, and that the total expense for all costs cannot exceed $100,000. Findthe maximum production level for the firm.(3) Compute the production level at x = 64 and y = 81. If the capital isdecreased by 3 units, by how many units the labor should be adjusted toso that there is not change in production level.
A small consulting firm is only interested in hiring graduates (denoted by S), but it does not know how many it should hire in order to be profit maximizing. Assume there is a competitive wage of $20 per hour and the production function is F(S)= 100S – (1/8)S2 . Hiring additional workers will increase production F(S) over relevant ranges of S. But is the 51st S more valuable than the 50th S in terms of her additions to overall production? What quantity of graduates should this firm hire and why does it stop hiring at this level of S? How does your answer change if the production function is F(S)= 200S –(1/8)S2 and the wage increases to $22?

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