Download Economics 101 L

Economics 101 L
Homework No. 9 – Solution Key
(Due in lab Nov. 3, 2008 for sections 1 & 3. Due in lab Nov. 5, 2008 for section 2.)
WORTH 100 POINTS TOTAL
1.
WORTH 20 POINTS – 5 POINTS EACH
a) Is a firm in a competitive industry considered a price taker or a price setter? Explain what this means.
Price taker. This means that the firm does not have any power to set the price for the good in the
market. Whatever price the market determines is the price that the firm must charge.
b) Is a monopolistic firm considered a price taker or a price setter? Explain what this means.
Price setter. A firm with monopoly power can charge whatever it wants for a particular price.
This is usually because there is only one firm in the industry or only a few.
c) Does a firm with monopoly power in a given industry produce more or less output than if the industry
was perfectly competitive? Why?
Less. Each firm produces where marginal revenue equals marginal cost. However, the marginal
revenue curve for a monopoly lies below its demand curve. The intersection of these curves is
always at a lower quantity of output than the intersection of the demand and marginal cost curve
for a competitive firm.
d) Explain what is meant by price discrimination.
Price discrimination refers to the ability of a monopoly to charge different prices to different
customers so as to realize a higher producer surplus.
2. Table A gives the total costs for a typical firm in a competitive industry. Table B gives the quantity
demanded at varying prices in the market. WORTH 30 POINTS
Table A
Quantity
0
1
2
3
4
5
6
7
8
9
10
Total
Cost
20
21
24
29
36
45
56
69
84
101
120
Table B
Marg.
Rev.
11
11
11
11
11
11
11
11
11
11
11
Marg.
Cost
1
3
5
7
9
11
13
15
17
19
Marg.
Rev.
Monopoly
23
19
15
11
7
3
Quantity
0
1
2
3
4
5
6
7
8
9
10
Price
23
21
19
17
15
13
11
9
7
5
3
Part A
1) Suppose that the price per unit of output is $11. Using excel, add a column for marginal cost and a
column for marginal revenue to Table A. 2 POINTS
See above table.
2) Graph the inverse supply and inverse demand curves for this firm. (Remember the relationship
between marginal cost and supply.) 4 POINTS
See Graph Below
2
Supply/Demand
25
Price
20
15
Demand
Supply
MR
10
5
0
0
1
2
3
4
5
6
7
8
9
10
11
Quantity
3) Add to the graph, the line representing marginal revenue. 2 POINTS
See graph above.
4) What is the profit-maximizing level of output? 2 POINTS
6 units
5) Calculate the consumer surplus. 2 POINTS
=(23-11)*6*0.5 = $36
6) Is there deadweight loss? If so, how much? 2 POINTS
No deadweight loss in perfectly competitive markets.
Part B – Now suppose a firm is able to monopolize this industry.
1) The equation for the inverse demand curve for this firm is P = 23 – 2Q. What is the equation
for the marginal revenue curve for the monopoly? 2 POINTS
P = 23 – 4Q
2) From Table A above, add a column for marginal cost and a column for marginal revenue for
this monopoly. Hint: Use the equation you found in the previous question for marginal
revenue. Note: Delete any negative values you get. 2 POINTS
See table above.
3) Create a new graph for this monopoly including the inverse supply and inverse demand curves
as well as the marginal revenue curve. 4 POINTS
See Graph Below
Monopoly
25
20
15
Price
Demand
Supply
MR
10
5
0
0
1
2
3
4
5
6
7
8
9
10
11
Quantity
4) What is the profit-maximizing level of output for this monopoly? 2 POINTS
3
4 units
5) What price does the monopoly receive for the good at this level of output? 2 POINTS
$15
6) Calculate the consumer surplus. 2 POINTS
=(23-15)*4*0.5 = $16
7) Is there deadweight loss? If so, how much? (The graph should help you see this.) 2 POINTS
Yes. = (15-7)*2*0.5 = $8.
3. Fill in the missing data on a monopolist in the following table: WORTH 20 POINTS – 4 POINTS EACH
Quantity
of Output
1
2
3
4
5
6
7
8
a)
b)
c)
d)
e)
Price
20.00
18.50
17.00
15.50
14.00
12.50
11.00
9.50
Total
Revenue
20
37
51
62
70
75
77
76
Marginal
Revenue
17
14
11
8
5
2
-1
Total
Cost
16
20
25
33
42
53
68
88
Marginal
Cost
4
5
8
9
11
15
20
Profit
4
17
26
29
28
22
9
-12
At what quantity will the monopolist produce in order to maximize profits? 4 units
What will be the price at this level of output?
$15.50
What will be the profits? $29
What quantity maximizes total revenue? 7 units
Explain in words why the quantity that maximizes profits is not the same as the quantity that
maximizes total revenue. Costs must be considered when maximizing profit. Thus, for
profit maximization, output is where MR=MC. Maximizing total revenue does not take
into account the cost associated with that level of output.
4. Suppose the ethanol industry exhibits monopolistic behavior. The government wants to encourage a
monopolist in this industry to produce more ethanol by paying a subsidy (a negative tax) for each unit produced.
WORTH 30 POINTS
a.
Neatly, on paper, draw a diagram (with quantity on the horizontal axis and price on the vertical
axis) representing the initial situation before the subsidy is introduced. (Your graph should contain
a linear inverse demand curve, a linear marginal cost curve, and a linear marginal revenue curve.)
10 POINTS
See graph below
(You may also do this problem in excel if you wish—whichever is easier for you.)
b.
c.
d.
e.
f.
g.
h.
On your graph, label the profit maximizing level of output prior to the subsidy. Call this Qm1
2 POINTS
Label the price the monopoly charges prior to the subsidy. Call this P m1
2 POINTS
Label the equilibrium price and quantity if this industry was perfectly competitive. Call these Q c
and Pc
2 POINTS
Now show the effect of the subsidy. Hint: remember how a tax affects a firm’s supply curve and
keep in mind that a subsidy can be thought of as a negative tax—having the opposite effect.
5 POINTS
Label the profit maximizing level of output after the subsidy is introduced. Call this Qm2
2 POINTS
Label the price the monopoly charges with the subsidy in place. Call this P m2
2 POINTS
On your diagram, show how deadweight loss changes from the scenario without the subsidy to the
scenario with the subsidy. 5 POINTS
4
The deadweight loss is originally the larger brown triangle. After the subsidy, the
deadweight loss becomes the smaller yellow triangle.
1.2
MC1
MC2
Pm1
Pm2
Pc
MR
D
0
0
Qm1
Qm2
Qc
1.2