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Economics 304
Homework #2 – The market for labor (Chapter 3)
Due Friday, 9/18 at the beginning of class– – no late papers accepted!

Instructions: Please show all work or points will be taken off. Good luck!

1. (50 points total – 5 points for each of 8 parts plus 10 for part i

The production function of a firm is given in the table below.

Number of workers

Units of output

MPN

0

0

1

48

2

84

3

108

4

128

5

143

6

155

7

165

a. Define the marginal product of labor and explain how it relates to the production function (with N on horizontal axis and Y on vertical axis). What shape does a production function typically take and why?

b. Fill in the MPN column. Does this production function have the typical shape that you identified above. Why or why not?

c. Assume that the price of a unit of output is $10 and the nominal wage that you pay is $210. Calculate the number of workers that you will hire and the associated profit in REAL terms (as we did in class, we ‘assume away’ all other costs of production).

d. Suppose that you are producing a commodity that you sell to China and given the slowdown in China’s economy, the price of your product falls to $7. Explain how and why you would change your behavior. Please provide the intuition beginning your answer with… at the same level of labor input I am no longer ……… (please be as specific as possible).

e. Calculate the new level of profits in REAL terms given the fall in price.

f. Suppose that you have debt and that the payment is $200 per period. Calculate the percent of profits that $ 200 represents given the conditions in part c. and then calculate the percent of profits that $200 represents given the conditions in d.

g. Suppose that profits and stock prices together as they usually do and that you own stock in this company. If you had a crystal and predicted the slowdown in China, would you sell stock before China slows down or would you hold on and sell the stock after China slows down?

h. Let’s return to the original conditions as in part c. Suppose that through research and development, you discover a new and abundant supply of your commodity so that the marginal product of labor for each worker rises by 2. Given this development. fill in table below.

Number of workers

Units of output

MPN

0

0

1

2

3

4

5

6

7

i. (10 points) Given that the workers are more productive, they demand a pay increase and you give it to them. The wage that is agreed upon is $220. Calculate the following:

Employment: Before and after the changes in parts h. and i.

Output: Before and after the changes in parts h. and i.

Profits: Before and after the changes in parts h. and i.

Real Wages: Before and after the changes in parts h. and i.

What are the implications of this change in conditions on the government budget?

2. (50 points total – 5 for each of 8 parts and 10 for diagram)

We know that there has been quite a bit of talk about the minimums wage. Below is a title of an article from the WSJ from 9/11/2015

NY gov’s call for $15 minimum wage faces major challenges
Updated Sept. 11, 2015 10:45 a.m. ET

Suppose the marginal productivity of labor curve is given as follows:

MPN = 58 – 3N.

The labor supply curve for federal employees is estimated to be:

NS = 10 + w

N is denominated in hundreds of workers (if you come up with a fraction of a worker round down to the nearest integer)

2a) Compute equilibrium values for the real wage and employment.

Illustrate this equilibrium on a labor market diagram in real wage space. Please be sure you label the diagram completely and label this initial equilibrium point as point A.

A correct and completely labeled diagram is worth 10 points

2b) Now we consider what would happen if the $15 minimum wage was imposed on this firm. What is the level of employment now? Assume that the price level is 1.00 so that 15 is the real wage.

2c) Compare the number of people willing to work vs. the number of people that are hired. What do we call the difference in these values when the quantity of labor supplied exceeds the quantity of labor demanded? Add these two points to your diagram and label these points as point(s) B. Make sure you identify the unemployed in your diagram.

2d) The intuition part 1: Why exactly did we move along the labor demand curve? In particular, why does the profit maximizing level of labor input change with the minimum wage program (make sure you write out the profit maximizing condition and explain why it has changed i.e., why do employers rationally change their quantity demanded of labor the way they did)?

2e) The intuition part 2. We also experience a movement along the labor supply curve. Explain the intuition here as in why are more people are willing to work using and explaining the substitution and income effects associated with labor supply. Which effect dominates and what has happened to the price of leisure for those that are still working, given the executive order?

2f) Suppose now that instead of raising the minimum wage, the governor of NY offers a training program that increase the marginal product of labor (an increase in human capital!) The new marginal product of labor is now:

MPN = 90 – 3N.

Find the equilibrium ‘market’ clearing wage and level of employment. Please show all work below.

Please depict this new development on your original diagram labeling this new equilibrium point as point C. Be sure to label diagram completely.

2g) Compare the welfare of the workers under the two scenarios: 1) the minimum wage program vs. 2) no minimum wage program but with the training program. In other words, are workers better off in part b) or are they better off in part f)? Be sure to explain.

2h) Compare the welfare of the firm, the employer. Is the firm better off in terms of profits in part b) or in part f)? Be sure to explain (feel free to refer to the plastering example and/or the new economy).

3. (40 points total – 5 for each of five parts and 15 points for diagram)

An economy’s aggregate production function is given by Y = A·K·N – N2. The marginal product of labor for this production function is MPN = A·K – 2N.

(a) Assume that A = 10 and K = 10. Suppose that the labor supply function for this economy is given by NS = 10 + 2w. Find the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy.

Draw a production function and labor demand curve vertically as we did in class (many times) and label this initial equilibrium point as point A.

A correct and completely labeled diagram is worth 15 points

(b) Suppose that a new innovation leads to an increase in total factor productivity so that A increases to 12. Everything else remains as in part (a). Find the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label on your diagrams as point B.

(c) Let’s go back to our initial conditions (point A). Instead of a new innovation impacting the economy, assume that severe weather destroys a portion of the capital stock, so that K = 8. Everything else is as it was in part (a). (In particular, A = 10.) Find the new levels of the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label (on both diagrams) as point C.

(d) Instead of a new innovation or bad weather impacting the economy (we are back to point A), suppose that there is a change in the supply of labor so that NS = 5 + 2w (All else remains as in part (a)). (In particular, A = 10 and K = 10.) Find the new levels of the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label on your diagrams as point D.

e) Give two well supported answers as to why Ns might have changed as it did in part (d) above.

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