Name:____Solutions______
SE201: PRINCIPLES OF MICROECONOMICS
Assignment 12: Due Wednesday, 12/9



Make sure you show your work and that ALL answers are complete and neatly
written.
Only work that follows these instructions and represents a “Good Faith Effort” to
answer the questions posed will receive a check. (Copying answers from a classmate
without working through the problems is unacceptable conduct).
Stop by during my office hours (MW period 5, 6) if you have questions, or set up
another time to meet with me.
Read Chapters 18 and 21 of your textbook. Answer the following questions that cover factor
markets and consumer theory.
From Chapter 18 (The Markets for Factors of Production) in the textbook:
4.
Smiling Cow Dairy can sell all the milk it wants for $4 a gallon, and it can rent
all the robots it wants to milk the cows at a capital rental price of $100 a day. It
faces the following production schedule:
# Robots
0
1
2
3
4
5
6
Total Output
0 gallons
50
85
115
140
150
155
MP
----
VMP
----
a. In what kind of market structure does the firm sell its output? Explain.
Because the firm can sell all of the milk it wants to at the market price of $4 per
gallon, Smiling Cow Dairy operates in a perfectly competitive output market.
b. In what kind of market structure does the firm rent robots? Explain.
Because the firm can rent all the robots it wants to at the market price of $100 per
day, Smiling Cow Dairy rents robots in a perfectly competitive market.
c. Calculate the marginal product and the value of the marginal product for each
additional robot.
The table below shows the MP and VMP for robots:
# Robots
0
1
2
3
4
5
6
Total Output
0 gallons
50
85
115
140
150
155
MP
---50 gallons
35
30
25
10
5
VMP
---$ 200
140
120
100
40
20
d. How many robots should the firm rent? Explain.
The firm should rent robots up to the point where VMP is equal to the rental price
(the robot wage). Therefore, it should rent 4 robots.
5. The nation of Ectenia has twenty competitive apple orchards, which sell apples at the
world price of $2 per apple. The following equations describe the production function
and marginal product of labor in each orchard:
Q = 100L – L2
MPL = 100 – 2L
where Q is the number of apples produced in a day, L is the number of workers, and
MPL is the marginal product of labor.
a. What is each orchard’slabor demand as a function of the daily wage W (Hint:
Remember that w = VMP if the firm is employing the optimal quantity of an input)?
What is the market’s labor demand curve (Hint: The market demand for a good is the
horizontal summation (summing over quantity) of individual demand curves)?
The firm’s demand for labor is the same as its value of the marginal product. The
firm will set wage equal to VMP:
w = VMP = P  MPL = 2(100 – 2L) = 200 – 4L
The market demand curve for labor will be the horizontal summation of the 20 firm
demand curves (summed across L).
Rearranging the firm’s demand, we get L = 50 – 0.25w. Thus, the market demand
curve must be L = 20(50 – 0.25w) = 1,000 – 5w.
Or, rearranging, we get w = 200 – 0.2L.
b. Ectenia has 200 workers who supply their labor (perfectly) inelastically. Solve for the
equilibrium market wage W. How many workers does each orchard hire? How much
profit does each orchard owner make?
If labor supply is inelastic at 200, then we can solve for wage by determining the
market equilibrium:
200 = 1,000 – 5w
w = 160.
Each firm will hire 10 workers (200 workers/20 orchards) and produce Q = 100(10) –
(10)2 = 900 apples. Total revenue for each firm will be (2)(900) = 1,800. Assuming
that wages are the firm’s only costs, total costs will be (160)(10) = 1,600, leaving
each firm with profit = 200. Total income for the country will be (200)(160) +
(20)(200) = 36,000.
From Chapter 21 (The Theory of Consumer Choice) in the textbook:
13. Five consumers have the following marginal utility of apples and pears:
Claire
Phil
Haley
Alex
Luke
Marginal Utility
of Apples
6
6
6
3
3
Marginal Utility of
Pears
12
6
3
6
12
The price of an apple is $1, and the price of a pear is $2. Which, if any, of these
consumers are optimizing over their choice of fruit? For those who are not, how
should they change their spending?
Utility is maximized when the marginal utility per dollar spent is equal across goods.
Claire and Alex are both purchasing the utility-maximizing combination of apples
and pears. Phil and Haley each get greater utility per dollar spent on apples than on
pears. Therefore, they should purchase more apples and fewer pears. On the other
hand, Luke gets higher utility per dollar spent on pears than on apples. He should
reallocate his budget as well, increasing his purchases of pears and reducing his
purchases of apples.