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Econ 443

Autumn 2023

Homework 6

1.  This is question 4 from Homework 5.  If you didn’t do the tasks that are highlighted on HW5 you can redo the problem with those tasks completed.

BLS data in Stata

a.  Retrieve the following series of data for the period January 1948 to September 2023 to September on separate graphs.  Data are from Table 1 of CPS Historical Data.   All should be seasonally adjusted.

(a) Unemployment rate of women age 20-plus

(b) Unemployment rate of men age 20-plus

(c) Unemployment rate, both sexes, age 16-19

(i.)  Download the Excel files, edit the excel files so you have a single file that can be readily transferred to Stata.

You will have to make sure that the series are aligned over time.

These should be the last twelve lines of your excel file.   Columns are “year”, “month” “UR_men”, “UR_women”, “UR_teen”.

ii.) Write a .do file that transfers the data in Stata and graphs the three series over time on a single graph. Generate a variable “time” which is a continuous measure of time and use that for the variable on the horizontal axis. Generate a variable “difference” which is the difference between men’s and women’s unemployment rate.  Graph “difference” against time.

2.  Factory, Inc.  is a monopsony in the market for labor in Springfield, USA.  Factory faces an (inverse) labor supply function of:

W = 40 + (.5) E

This implies that the marginal cost of labor curve is:

MC_E = 40 +  E

Factory’s (inverse) demand curve for labor is:

W =  200 – E

a.  Suppose that Factory is a non-discriminating monopsonist.   He will choose hire labor at the point where the marginal cost of an employee equals the value of the marginal product of an employee.

i.)  Calculate Factory’ profit maximizing level of labor.

ii.)  What wage will Factory pay?

iii.)  Illustrate your answer in a diagram.  Graph the labor supply, marginal cost of employment and labor demand curves.  Indicate the amount of labor employed and the wage rate on the graph.  Indicate the producer surplus, the worker surplus, and the deadweight loss.  Are any of these three numbers zero?  Which one(s)?

b. Suppose that Factory is a discriminating monopsonist.  How many employees will Factory hire? On another diagram, indicate the firms’ surplus, the workers’ surplus, and the deadweight loss.  Are any of these three numbers zero?  Which one(s)?

3.  Suppose the inverse demand curve for labor is:

W = 1000 – 12E

and the inverse supply curve is:

W = 100 + E²

(notice the exponent on “E”)

and the market is a monopsony.

a.  What is the expression for the marginal cost of labor if the market is a non-discriminating monopsony?

b.  How much labor will this non-discriminating monopsony employ maximize profits?

c. What will the non-discriminating monopsony pay?

d. Illustrate your answer in a diagram.

e. How much labor will the monopsony use to maximize profits if it is a perfectly discriminating monopsony?

f.  Illustrate your solution in a diagram.  Illustrate producer surplus, worker surplus and deadweight loss in each case.

Hint:  You will need to apply the quadratic formula to solve parts (b) and (d).  The quadratic formula is:

(Old) Borjas problem

In a particular industry, labor supply is E_S = 10 + w and labor demand is E_D = 40 - 4w, where E is the level of employment and w is the hourly wage.

(a) What is the equilibrium wage and employment if the labor market is competitive? What is the unemployment rate?

(b) Suppose the government sets a minimum hourly wage of $8. How many workers would lose their jobs? How many additional workers would want a job at the minimum wage? What is the unemployment rate?

Submitting your solutions to Question 1.    Copy and paste your .do file, .log file and any graphs into a Word file.  Convert the Word file to .pdf and submit the .pdf.  Your .do file and .log file names should include your name.   The title of the graph should include your name.   Indicate how you ran the program. (Downloaded from Stata site and used in a Windows system, downloaded from Stata site and used in a Mac system, used CSDE server.)

The document Econ443_Au23_Lecture8_Stata_21Oct23 has a template for a .do file.   There is a tutorial that goes through the document posted on Canvas.