2. (Textbook problem 6, page 104) Suppose that the production function is Y = 9K 0.5 Nº.5. With this production function, the marginal product of labor is MPN = 4.5K0.5 N -0.5 The capital stock is K = 25. The labor supply curve is NS = 100[(1-t) w]², where w is the real wage rate, t is the tax rate on labor income, and hence (1-t) w is the after-tax real wage rate. a. Assume that the tax rate on labor income, t, equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers. b. Repeat part (a) under the assumption that the tax rate on labor income, t, equals 0.6. c. Suppose that a minimum wage of w = 2 is imposed. If the tax rate on labor income, t, equals zero, what are the resulting values of employment and the real wage? Does the introduction of the minimum wage increase the total income of workers, taken as a group?

2. (Textbook problem 6, page 104) Suppose that the production function is Y = 9K 0.5 Nº.5. With this production function, the marginal product of labor is MPN = 4.5K0.5 N -0.5 The capital stock is K = 25. The labor supply curve is NS = 100[(1-t) w]², where w is the real wage rate, t is the tax rate on labor income, and hence (1-t) w is the after-tax real wage rate. a. Assume that the tax rate on labor income, t, equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers. b. Repeat part (a) under the assumption that the tax rate on labor income, t, equals 0.6. c. Suppose that a minimum wage of w = 2 is imposed. If the tax rate on labor income, t, equals zero, what are the resulting values of employment and the real wage? Does the introduction of the minimum wage increase the total income of workers, taken as a group?

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 9PA

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6. In a certain factory, the daily output is Q = 60 K1/2 L1/3 units, where K represents the invested capital measured in thousands of pesos and L the size of the force of work measured in worker-hours. Determine the marginal product functions of the labor and capital.
6. Suppose the hourly wage is $40, the price of each unit of capital is $50, and the price of output is $100 per unit. Assume that the firm cannot affect any of these prices. The production function of the firm is f(E,K) = JE× K, so that the marginal product of labor is JK MPE 2VE a. If the current capital stock is fixed at 1,600 units, how many hours of labor should the firm hire in the short run (i.e., what should E be)? b. Set up the profit function. How much profit will the firm earn? c. Now suppose that the price of labor increases to $50/hour. Find the new optimal level of employment. We remain in the short term, so the level of capital remains fixed. d. What is the short run elasticity of labor demand? Is labor demand elastic or inelastic?
4) If the marginal product of capital MPK > r, where r is the market rental rate for capital, the firm A. Should hire more capital until MPK = r. B. Should hire more labor until MPK = r. C. Should hire more labor until MPK = 0. D. Should fire more capital until MPK = r. %3D 5) Figure 1 below shows the dynamics of per-capita GDP for six countries in ratio scale from 1870 to 2010. From the Figure we learn that the level of per capita GDP A. Has almost doubled for the US from 1880 to 2020 B. Was higher in the U.S. compared to the UK in 1880 C. Was higher in China compared to Argentina in 2000. D. Increased by approximately 5 times in Japan from 1950 to 1970. Answer 64,000 U.S. 32,000 16,000 Argentina 8,000 U.K. 4,000 Japan 2,000 S. Africa China 1,000 1880 1900 1920 1940 1960 1980 2000 2020
Course: Introduction to Economics - Labor Market This exercise is presented again. There are still no answers. Please, I need a real expert. Thank you You've been asked to solve an analytical example to illustrate concretely effects of minimum wage and labor income tax legislation on employment and, therefore, unemployment. For this, you have decided to study Labor Demand of a firm whose production function is given by: Y = A K1/3 L2/3For simplicity, you decide to assume that A = P = K = 1 , where A is factor productivity, P is price of the good sold by firm and K is amount of capital hired by firm. Recall, moreover, that optimal decision of any economic agent can be reduced to an equality between marginal revenue and marginal costs. In particular, firm will hire workers up to a point where marginal revenue (MR) of their labor equals marginal cost (MC). Given production function you have decided to use for analysis, marginal productivity (MPL) of labor is given by: MPL =…
20. (Figure: Capital and Labor XVI) Consider the production function Q = 10.5K0.5, with MP k = L0.5/K0.5 and MPL = K0.5/10.5 Capital (K) 90 81 a. -81 5 The slope of the isoquant at Point A is b. 81 c. -9 70 60 50 40 30 20 9 d. 9 0 B Q=9 9 10 Labor (I)
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7 Question 7 For each of the following functions, does the function satisfy all properties of a short run output- constrained labor demand function? If it does, demonstrate that it satisfies all properties. If not, show at least one property that it violates. 1. L * (q, w, r, K) = w(q − K) when q ≥ K and L * (q, w, r, K) = 0 when q ≤ K. 2. L* (q, w, r, K) = }
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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)).
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