EBK MACROECONOMICS
EBK MACROECONOMICS
10th Edition
ISBN: 9780134896571
Author: CROUSHORE
Publisher: VST
Question
Book Icon
Chapter 3, Problem 6NP

a)

To determine

To find the equation of the labor demand curve, the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers.

a)

Expert Solution
Check Mark

Explanation of Solution

Given,

The production function:

  Y=9K0.5N0.5

  MPN=4.5K0.5N0.5

The amount of capital is 25.

The labor supply curve:

  NS=100[(1t)W]2

Where, ‘W’ is the real wage rate and ‘t’ is the tax rate on labor income.

Since MPN = W

  W=4.5K0.5N0.5N0.5=W4.5K 0.5N=[ 4.5 K 0.5 W]2N=20.25KW2

  N=20.25×25W2=506.25W2

If t = 0, then labor supply is:

  NS=100W2

At equilibrium, labor supply is equal to the labor demand. Setting labor supply equal to labor demand gives

  NS=ND100W2=506.25W2W4=5.0625W=1.5

If W = 1.5, then labor supply is:

  NS=100 ×(1.5)2=225

  N=506.25 1.52=225

  Y=9K0.5N0.5=9×250.5×2250.5=45×15=675

The total after-tax wage income of workers is:

NS × (1-t)W, which is equal to 337.5(225×1.5).

b)

To determine

To find the equation of the labor demand curve, the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers, when t = 0.6.

b)

Expert Solution
Check Mark

Explanation of Solution

From the previous part, marginal product of labor is:

  MPN=4.5K0.5N0.5W=4.5×250.5N0.5=22.5N 0.5

  N=100[( 1t) 22.5 N 0.5 ]2N=100[( 10.6) 22.5 N 0.5 ]2N=100( 81N)N2=8100N=90

If t = 0.6, then labor supply is:

  NS=100[( 1t)W]2=100[( 10.6)W]2=16W2

  W=22.5N 0.5=22.5 90 0.5=2.37

  Y=9K0.5N0.5=9×250.5×900.5=426.91

The total after-tax wage income of workers is:

NS × (1-t)W, which is equal to 85.38 (90 × 0.4×2.37).

Here, output and income both decreases, although the wage is higher.

c)

To determine

The value of employment and real wage, when w = 2 and t = 0.

c)

Expert Solution
Check Mark

Explanation of Solution

The minimum wage w = 2 and tax rate t = 0.

  N=506.25W2=506.2522=126.6

If t = 0, then labor supply is:

  NS=100W2

  NS=100×22=400

Since labor supply is equal to 400 and labor demand is equal to 126.6, so labor supply exceeds labor demand.

  Unemployment=400126.6=273.4

Total income of the workers is:

wage × N = 2 × 126.6 = 253.2,which is lower than without a minimum wage (= 337.5), because employment has declined so much.

Therefore, introduction of minimum wage decreases the total income of workers.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
6. Rent seeking The following graph shows the demand, marginal revenue, and marginal cost curves for a single-price monopolist that produces a drug that helps relieve arthritis pain. Place the grey point (star symbol) in the appropriate location on the graph to indicate the monopoly outcome such that the dashed lines reveal the profit-maximizing price and quantity of a single-price monopolist. Then, use the green rectangle (triangle symbols) to show the profits earned by the monopolist. 18 200 20 16 16 14 PRICE (Dollars per dose) 12 10 10 8 4 2 MC = ATC MR Demand 0 0 5 10 15 20 25 30 35 40 45 50 QUANTITY (Millions of doses per year) Monopoly Outcome Monopoly Profits Suppose that should the patent on this particular drug expire, the market would become perfectly competitive, with new firms immediately entering the market with essentially identical products. Further suppose that in this case the original firm will hire lobbyists and make donations to several key politicians to extend its…
Consider a call option on a stock that does not pay dividends. The stock price is $100 per share, and the risk-free interest rate is 10%. The call strike is $100 (at the money). The stock moves randomly with u=2 and d=0.5. 1. Write the system of equations to replicate the option using A shares and B bonds. 2. Solve the system of equations and determine the number of shares and the number of bonds needed to replicate the option. Show your answer with 4 decimal places (x.xxxx); do not round intermediate calculations. This is easy to do in Excel. A = B = 3. Use A shares and B bonds from the prior question to calculate the premium on the option. Again, do not round intermediate calculations and show your answer with 4 decimal places. Call premium =
Answer these questions using replication or the risk neutral probability. Both methods will produce the same answer. Show your work to receive credit. 6. What is the premium of a call with a higher strike. Show your work to receive credit; do not round intermediate calculations. S0 = $100, u=2, d=0.5, r=10%, strike=$150
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Exploring Economics
Economics
ISBN:9781544336329
Author:Robert L. Sexton
Publisher:SAGE Publications, Inc
Text book image
Managerial Economics: Applications, Strategies an...
Economics
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:Cengage Learning
Text book image
Survey of Economics (MindTap Course List)
Economics
ISBN:9781305260948
Author:Irvin B. Tucker
Publisher:Cengage Learning
Text book image
Economics (MindTap Course List)
Economics
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Cengage Learning
Text book image
Macroeconomics
Economics
ISBN:9781337617390
Author:Roger A. Arnold
Publisher:Cengage Learning
Text book image
Microeconomics: Private and Public Choice (MindTa...
Economics
ISBN:9781305506893
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:Cengage Learning