MBA 5322 Midterm Exam - In a competitive labor market, demand

1. (12 points) In a competitive labor market, demand for workers is QD 10,000 – 100W, and supply is QS
2,000 1,900W, where Q is the quantity of workers employed and W is the hourly wage. What is
the initial equilibrium wage and employment level? Suppose that the government decides that $5 per
hour is the minimum allowable wage in any market. How would this new minimum wage alter this
market? What would the new employment level be? What would happen to total payments to labor?
Would there be any excess supply of labor? If so, how much?
2. (12 points) Suppose demand for inkjet printers is estimated to be Q 1000 – 5p 10pX – 2pZ 0.1Y.
If p 80,
pX 50, pZ 150, and Y 20,000; answer the following:
a. What is the price elasticity of demand?
b. What is the cross price elasticity with respect to commodity X? Give an example of what
commodity X might be.
c. What is the cross price elasticity with respect to commodity Z? Give an example of what
commodity Z might be.
d. What is the income elasticity?
3. (16 points) Suppose a consumer has income of $240 per period, and faces prices pX 4 and pZ 6.
Her goal is to maximize her utility, described by the function U 20X 0.3Z 0.7. Calculate the utility
maximizing bundle (X *, Z *). What happens to the optimal bundle if price of good z drops to 3?
4. (10 points)Assume a consumer’s utility function is described by U 2X Z, and prices are pX 2
and pZ 1, what is the solution to her utility maximization problem? What does this tell you about X
and Z as commodities? (Hint: draw a graph showing a budget constraint and indifference curve
using the information provided.) 1 5. (18 points) Draw a graph with arcade games on the horizontal axis and newspapers on the vertical
axis. Joe has $10 per week to allocate between these commodities. The price of newspapers is $0.50.
At the initial price for arcade games of $0.25, Joe purchases 10 newspapers and plays 20 games.
When the price of games increases to $0.50, Joe purchases 8 newspapers and plays 12 games. When
the price of games increases again to $0.75, Joe buys 5 papers and plays 10 games.
a. Use this information to draw the utility maximizing points on a graph.
b. Draw the individual demand curve for arcade games.
c. Use the information given to calculate Joe’s elasticity of demand for arcade games between
$0.25 and $0.50, and between $0.50 and $0.75.
6. (12 points) Use the labor/leisure model to analyze the effect on hours of work of a law requiring
employers to pay time and a half for hours worked over 40 per week.
a. Draw a budget constraint for someone earning $8 per hour who receives $100 a week in
non-labor income. What happens to the budget constraint with the time-and-a-half
requirement?
b. Given your answer to (a) draw an indifference curve so that, given the original budget
constraint, the person is working 40 hours per week. What happens to hours of work
given the new budget constraint? Draw an indifference curve that shows this. Have
hours of work increase or decrease as a result of this overtime law? Explain why 2 7. (21 points) Researchers have found that alcohol consumption have positive and negative effects
on people’s health. For instance, some researchers argue that red wine consumption decreases
heart disease problems. On the other hand, some studies have found that excessive consumption
of red wine severely affects the liver of heavy drinkers.
A government official finds out you are familiar with linear regression analysis and asks you to
verify the information provided in the previous paragraph. She provides you with the following
information:
"Australia"
"Austria"
"Belg/Lux"
"Canada"
"Denmark"
"Finland"
"France"
"Iceland"
"Ireland"
"Israel"
"Italy"
"Japan"
"Netherlands"
"New Zealand"
"Norway"
"Spain"
"Sweden"
"Switzerland"
"UK"
"US"
"West Germany" Alcohol
2.5
3.9
2.9
2.4
2.9
0.8
9.1
0.8
0.7
0.6
7.9
1.5
1.8
1.9
0.8
6.5
1.6
5.8
1.3
1.2
2.7 Heart
211
167
131
191
220
297
71
211
300
183
107
36
167
266
227
86
207
115
285
199
172 Where:
Alcohol = consumption per capita of red wine (in liters).
Heart = heart disease deaths per 100,000 inhabitants.
Liver = liver disease deaths per 100,000 inhabitants. 3 Liver
15.3
45.6
20.7
16.4
23.9
19
37.9
11.2
6.5
13.7
42.2
23.2
9.2
7.7
12.2
36.4
11.2
20.3
10.3
22.1
36.7 Based on the previous table, answer the following questions based on the two equations:
i. = 0 + 1 ii. = 0 + 1 a. (4 points) What are the values of beta0, beta1, alpha0 and alpha1? Write down the two equations
with estimated coefficients.
b. (3 points) Are they statistically significant? Why?
c. (4 points) Interpret the value of beta1 and alpha1?
d. (3 points) Are the values of these coefficients (beta1 and alpha1) consistent with the story of the
first paragraph? Why?
e. (4 points) What is the value of the elasticity of liver diseases with respect to alcohol
consumption? Interpret.
f. (3 points) Is this coefficient reliable? Why? 4