Assignment:
(Use handout - Statistical Testing of Labor Market Hypotheses - for help with this problem.
1. Assume you are interested in analyzing the effect of educational attainment on wages. You interview a few people and come up with the following data set:
|
Individual
|
Education (years)
|
Wage ($/hour)
|
|
A
|
10
|
10
|
|
B
|
12
|
12
|
|
C
|
12
|
16
|
|
D
|
14
|
15
|
|
E
|
16
|
12
|
|
F
|
16
|
20
|
|
G
|
21
|
25
|
a. Graph the data, with wages on the y-axis and education on the x-axis. (You can use Excel if you like.) Be sure to attach the graph.
b. State the economic relationship you believe exists between an additional year of education and the hourly wage.
c. Your econometric model is: Wi + β0 + β1 Educi + errori. What is the interpretation of the intercept (β0) and the slope (β1). State both the economic and the math interpretations.
d. Assume that you estimate the equation in (c) using the above data. The resulting estimated equation is: Wˆi = -1.64 + 1.20 Educi with standard errors of 5.26 and 0.35 respectively, and an R-square of 0.697. What is the predicted wage of an individual with a high school diploma (i.e., 12 years of education)? What is the predicted wage of an individual with a bachelor's degree (i.e., 16 years of education)?Do your results make sense? Why or why not?
e. How would omitting an important independent variable, e.g., ability, affect your answers in (d)?
Answer both questions.
2. Go to the Bureau of Labor Force Statistics Internet site, https://www.bls.gov, type a tables in the search box in the upper-right-hand corner.Click on Table A-1, https://www.bls.gov/webapps/legacy/cpsatab1.htm. Check the box by "participation rate" for some group. Click on "retrieve data" (at the bottom of the page). On the top of this new page, you can change output options and choose different years as well as have the information presented in graphical form.
a. Use the ‘seasonally adjusted' option to answer the following questions. What were the labor force participation rates of men and women (20 years and over) in January 1950 and for the most recent month shown? Which rate has increased over this period, and which has declined? What are some possible explanations for these changes?
b. Use the ‘Seasonally adjusted' option to create graphs of men's and women's (20 years and over) labor force participation rates over the period, 1948 to 2018. Attach the graphs. What is interesting about these trends? Explain.
c. Go back to Table A-1. For the group, both sexes, 16 to 19 years, click on the civilian labor force level and unemployment level boxes (both are in blue rows), which gives you the number of teenagers (in thousands) in the labor force and unemployed. Use these numbers to calculate the teenage unemployment rates for January 2000, June 2009 and January 2019. What explains these differences? Be sure to show your work.
3. The following question is from your text. Ecuador is the world's leading exporter of bananas, which are grown and harvested by a large labor force that includes many children. Assume Ecuador now outlaws the use of child labor on banana plantations. Using economic theory in its ‘positive' mode, analyze what would happen to employment and wages in the banana farming industry in Ecuador. Use demand and supply curves in your analysis.
Answer both questions.
4. This question is based on your text's quantitative question. At the local widget factory, the firm can produce the following output per day at various employment levels.
|
Workers
|
Output
|
Marginal Product
|
Marginal Revenue Product
|
|
0
|
0
|
|
|
|
1
|
10
|
|
|
|
2
|
34
|
|
|
|
3
|
66
|
|
|
|
4
|
100
|
|
|
|
5
|
130
|
|
|
|
6
|
150
|
|
|
|
7
|
168
|
|
|
|
8
|
178
|
|
|
|
9
|
180
|
|
|
|
10
|
178
|
|
|
a. Calculate each worker's marginal product.
b. If the price per widget is $2, calculate the firm's Marginal Revenue Product.
c. Plot the marginal revenue product of labor against the number of workers. Which part of the graph shows diminishing marginal productivity to labor? Explain.
d. If the firm must pay $40/day, how many workers will the firm employ? Illustrate your answer with a graph.
e. What happens if the price per widget increases to $4? Explain.
5. Use substitution and scale effects to answer the following questions. Assume that labor is the only variable input in the short run. What causes employment (i.e., number or workers employed) to fall in the short run if the wage increases? What causes employment to fall in the long run if the wage increases?
6. In the US labor market, the labor supply function is: Ls = 50 + W + Xs , and the labor demand function is: LD = 150 - 3W + XD, where LS is the quantity of labor supplied at each wage, LD is the quantity of labor demanded, W is the hourly wage, XS is a non-wage variable affecting labor supplyand XD is a non-wage variable affecting labor demand (e.g., price of output).
a. Assuming XS=1 and XD=1, what is the equilibrium wage and employment if the labor market is competitive? What is the unemployment rate?
b. Given the ΔW / ΔLD = -1/3, use your answer in (a) calculate the wage elasticity of demand for labor at equilibrium.
c. Given the ΔW / ΔLs = 1, use your answer in (a) calculate the wage elasticity of supply for labor at equilibrium.
d. Suppose the government sets a minimum hourly wage of $30. How many workers would lose their jobs? How many additional workers would want a job at the minimum wage? What is the unemployment rate?
e. Illustrate your answers to (a) and (d) with a graph.
f. What happens to the supply curve for labor if XS increases? What is a likely candidate for XS?
g. What happens to the demand curve for labor if XD increases? What is a likely candidate for XD?