The market for labor and the production function

Econ 304

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185 total points

Economics 304

Homework #2 – The market for labor and the production function (Chapter 3)

Due Friday, 9/15 at the beginning of class – no late papers accepted!

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

1. (60 points total).

a) (5 points) Fill in the Table below.

Number of workers Units of output MPN
0
1 40
2 75
3 105
4 130
5 150
6 165
7 175

b. (10 points) 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? Does this production function take the ‘typical’ shape?

Consider the recent news on the value of the US dollar

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Assume that you sell your output to Europe for a US price = $10, and The exchange rate at the beginning of 2017 was one euro = $1.03 but for ease with the numbers, let’s round down to one euro equal $1.00. So the euro price of your product is 10 Euros. Answer the following questions.

c) (5 points) You can hire all the workers you want at $210 per worker. Along with the US price = $10, 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). Please give me the marginal REAL profit of each worker hired and then add them up and that is the total profit in real terms.

We now adjust for the change in the value of the US dollar relative to the euro – as the title of the article suggests, the current exchange rate is now one euro = $1.25

d)(5 points) What is the new Euro price of your product, assuming that your US dollar price stays at $10?

e).(5 points) Given the change in conditions you decide to raise the price of your product in US dollar terms so that the Euro price stays the same as it was before the change in the exchange rate. What is the new US dollar price? Please show all work.

f) (10 points) What has happened to the marginal revenue product (MRPN) for each worker (has it gone up or down?) and why given the change in price? Be sure to define what the marginal revenue product is and what it means in ‘laypersons’ terms.

g) (10 points) Given that the US$ price of your product has changed, 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). Again, explain in REAL terms, not nominal terms.

h. (5 points) Calculate the new level of profits in REAL terms given the change in condition including the change in the exchange rate, the change in the US $ price of your product. and the change in your behavior.

i)(5 points) The Treasury secretary Mnuchin and President Trump would argue that a weak dollar is good for firms and creates jobs – are your results consistent with the notion, why or why not? Explain!

2. (75 points total) Please show all work

Suppose the labor supply for a firm is given by:

NS = 5 + 2w

and REAL Labor Demand (MPN) is given by:

MPN = A K – 2 N

A = 10, K = 4

a)(5 points) Calculate the market clearing real wage and labor input (show work).

In the space below, draw a picture of this labor market labeling this initial equilibrium as point A. Be sure to label your graph completely.

15 points for correct and completely labeled diagram

b)(10 points) The local government votes on and passes a living wage ordinance, similar to a minimum wage, making it illegal to pay less than 20 in real terms – that is, the living wage is 20 – it is illegal for firms to pay less – we can assume we are in the base period so that nominal wages are the same as real wages. How many workers are willing to work at a real wage of 20 and how many workers are firms willing to hire? What do we call this difference?

Add these 2 points as points B on your diagram.

c)(10 points) Explain exactly why the firm changes their behavior given the governments decision to impose a living wage = 20. Start with at the same level of labor input…….

d)(5 points) Compare the number of people willing to work before and after the living wage legislation – why is this number so different?

e) (10 points) Suppose the local government decides not to pass the living wage ordinance and instead passes a bill where county workers have access to classes designed to increase their human capital and thus, increase their productivity. It works!

“K” which of course stands for human and physical capital rises to 7 (it was 4)

Resolve for the market clearing real wage and labor input and label this point as C on your graph.

f)(10 points) Now consider the movement from point A to point C on your graph. Explain why the firm changes their behavior – explain using specific numbers again starting your answer with at the same level of labor input…….

g)(5 points) Were workers better off with the living wage ordinance or with the classes that increase their human capital? Explain.

h)(5 points) Are firms better with the living wage ordinance or the training classes? Explain.

3. (50 points total – 5 for each of part and 15 points for completely labeled diagram.)

The following equations characterize a country’s closed economy.

Production function: Y = A·K·N – N2/2

Marginal product of labor: MPN = A·K – N.

where the initial values of A = 8 and K = 10.

The initial labor supply curve is given as: NS = 20 + 9w.

a) (10 points) Find the equilibrium levels of the real wage, employment and output (show work).

In the space below, draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph. Be sure to label everything including these initial equilibrium points as point A.

(15 points for correct and completely labeled diagrams)

We now have numerous changes to our economic conditions (all is not constant). Think of all these changes happening together, that is, we go from one state of economic affairs to a different state of economic affairs. Below are the changes.

· The labor supply changes and is now: NS = 24 + 9w .

· K goes down from 10 to 8.

b) (5 points) What could cause such a change in labor supply? Please give two specific and well supported reasons. Be sure to explain your answer.

c) (10 points) Solve for the new equilibrium values of the real wage, employment, and output and label as point B.

d)(10 points) Explain why exactly why the firm changes their behavior… again… at the same level of labor input ……….. Use specific numbers!

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