Economics 102
Question 1
Suppose the Kingdom of Atlantis decides to levy a
tax of one shekel on the production of each
widget.
(a) Demonstrate that the decline in consumer and
producer surplus resulting from the tax
exceeds the amount of tax revenue collected.
(b) Given the tax, what is the relationship between
the price paid by consumers and the marginal
cost of production?
A Tax and Economic Welfare
S with tax
No Tax
S w/o tax
A
Tax
Change
CS
ABCD
A
-(BCD)
PS
EFGH
H
-(EFG)
P1
Tax
Revenue
B
C
D
Zero
BCEF
BCEF
P0
E
G
F
W
ABCD
EFGH
ABCEF
H
-(DG)
P2
H
Q1
Q0
The area (DG) is the deadweight loss from the tax
• The decline in CS and PS is BCDEFG
while the level of tax revenue is BCEF
• The price paid by consumers (P1)
exceeds the price received by producers
(P2) and thus the price that consumers
pay exceeds MC
Question 2
•
•
•
•
Suppose now that the Kingdom eliminates the tax and
decides instead to subsidize the widget industry.
Suppose the subsidy equals one shekel for every
widget produced.
(a) Demonstrate that the increase in consumer and
producer surplus resulting from the subsidy is less
than the amount of money that the government gives
the producers.
(b) Given the subsidy, what is the relationship between
the price paid by consumers and the marginal cost of
production?
(c) Given your answers to (1a) , (1b), (2a), and (2b),
what is the “optimal” relationship (from society’s
overall point of view) between price and marginal cost?
Subsidies and Economic Welfare
S w/o Subsidy
Producer P3
Net Price with Subsidy
S w/ Subsidy
Amount Producers Receive
from Government
Equilibrium P1
Price Without Subsidy
Consumer P2
Price With Subsidy
Q1
Q2
Without
Subsidy
CS
AB
ABEFG
PS
EH
BCEH
Gov’t
EXP
S w/o Subsidy
With
Subsidy
W
zero
ABEH
BCDEFG
ABEH - D
Change
EFG
BC
BCDEFG
-D
A
Producer
P3
B
S w/ Subsidy
C
P1
E
Consumer
Amount Producers Receive from
Government
D
F
G
P2
AREA “D’ represents the Deadweight loss from the
subsidy
H
Q1
Q2
• The increase in CS and PS is BCEFG
• The cost of the subsidy program is
BCDEFG which is larger
• The price that consumers pay(P2) is less
than the net price that producers receive
(P3) and thus the price that consumers
pas is less than marginal cost
• The optimal outcome is when the price
that consumers pay equals MC
Question 3
•
Consider the
following cost
schedule:
Q
0
1
2
3
4
5
6
7
8
9
10
11
TC
100
122
140
155
175
200
230
265
305
350
400
455
• a) Assume the price of the product is $50. What
is the profit maximizing level of output?
• b) What is the lowest price at which the firm will
produce? Given this price, how many units
should the firm produce? Explain.
• C) What is the break-even price? Given this
price, how many units should the firm produce?
Explain.
Q
0
1
2
3
4
5
6
7
8
9
10
11
TC
100
122
140
155
175
200
230
265
305
350
400
455
AVC
22
20
18.33
18.75
20
21.67
23.57
25.63
27.78
30
32.27
ATC
122
70
51.67
43.75
40
38.33
37.86
38.13
38.89
40
41.36
MC
22
18
15
20
25
30
35
40
45
50
55
Profits are maximized when p=MC assuming P is greater than or equal to AVC.
Thus, when the price is 50, profits are maximized when Q = 10
The lowest price at which the firm will operate is the minimum AVC. In this case, this
is 18.33 when Q = 3
The breakeven price is the minimum ATC. In this case, this
is 37.86 when Q = 7
Question 4
4) Consider the nation of Atlantis which is populated by rational,
perfectly informed, identical individuals.
One of the staples of the diet is fish. To keep it affordable, the price of
fish is regulated below the market equilibrium price.
The Parliament of Atlantis is currently considering legislation that would
eliminate the price regulation. According to the Laissez Faire party,
the removal of the price control would improve resource allocation.
Opponents of the policy change argue that decontrol would reduce
the welfare of the typical inhabitant.
Upon hearing of your expertise in economics, the King has requested
your advice. Please advise him on this proposed change in policy
using the tools of analysis developed in this course.
Assume the maximum legal price is
P1
Price Decontrol
Control
CS
A
PS
A,C
G
B
P2
D
W
C
E
P1
G
F
A,C,G
Change
Price Decontrol
Control
CS
A
PS
A,B
A,C
G
C,D,G
B
P2
D
W
C
E
P1
G
F
A,C,G
A,B,C,
D,G
Change
Price Decontrol
Control
CS
A
PS
A,B
A,C
G
C,D,G
Change
B-C
C,D
B
P2
D
W
C
E
P1
G
F
A,C,G
A,B,C,
D,G
B,D
Question 5
5) To protect its domestic sneaker industry, the Kingdom of Atlantis
currently disallows imports of sneakers.
The Laissez-Faire party has proposed that the edict be revoked.
Based on the writings of Adam Smith, it is argued that free trade will
improve the allocation of resources.
The political party known as the Atlantis-First party opposes the
importation of foreign sneakers. They argue that permitting foreign
sneakers into Atlantis will enrich foreigners at the expense of the
typical Atlantian.
The Laissez-Faire party concedes that removing the edict will hurt the
domestic producers of sneakers. Yet, they maintain that Atlantis will
be better off, not worse off, if the edict if revoked.
Upon hearing of your expertise in the field of economics, the King has
requested your advice. Using the tools of analysis developed in
this course, what would you advise the King?
Ban
Domestic Supply
CS
A
A
PS
B,E
W
A,B,E
B
C
D
World Price
E
Demand
Trade
Permitted
Change
Ban
Trade
Permitted
Domestic Supply
CS
A
A,B,C,D
A
PS
B,E
W
A,B,E
E
B
C
D
World Price
E
A,B,C,D,E
Change
Ban
Trade
Permitted
Change
Domestic Supply
CS
A
A,B,C,D
B,C,D
E
-B
A
PS
B,E
W
A,B,E
B
C
D
World Price
E
A,B,C,D,E
C,D
Question 6
• (A) (i) Briefly explain why a price taker can
expected to produce at the output level where
MC = Price. (ii) How does this output level
compare to the point of diminishing marginal
returns to labor? (iii) How does this output level
compare to the point where ATC is minimized?
(iv) Are there any exceptions to this “rule?”
• (B) Why is it in society’s interests for producers
to operate at the point where MC = P ?
Profit = TR - TC
Δprofit = ΔTR - ΔTC
Divide both sides by the change in output, ΔQ
ΔProfit
ΔQ
ΔTR
ΔTC
ΔQ
ΔQ
=
Marginal Profit =
MR
-
MC
When Firms are price takers
• Marginal Revenue(MR) = Price
Thus,
Marginal Profit = P - MC
The Profit Frontier
Profit
The Slope of the Curve is the change in profits when
Output increases by one unit. In other words, the slope
Represents Marginal Profit
Marginal Profit
is zero at
This point
Marginal Profit is positive
At this point
Marginal Profit
is negative
At this point
0
Q*
Q
Profit Maximization when a Firm is
a Price Taker
• From the previous slide, it is clear that
profit maximization requires that a price
taker produce where Marginal Profits
equal zero
• But Marginal Profit equals P – MC
• Thus, profit maximization for a price taker
requires that a price taker produce where
MC = P
How does the profit maximizing level of output compare to
the point of diminishing marginal returns to labor?
• MPL is maximized at the point of
diminishing marginal returns to labor
• Given the inverse relationship between
MPL and MC, this means that MC is
minimized at the point of diminishing
marginal returns to labor
Suppose Price equals P5 and Q = Qo. Are
Profits at a Maximum?
MC
P5
ATC
AVC
Note that Price exceeds MC
When Q = Q0
Thus, marginal profits are positive
at Q0 which means that profits will
rise if more is produced
MC@Q0
Q0
How does the profit maximizing level of output compare to
the point of diminishing marginal returns to labor?
Based on the previous slide, the profit maximizing level of output is greater
Than the output level that corresponds to diminishing marginal returns
How does the profit maximizing
level of output compare to the point
where ATC is minimized?
Suppose Price equals P5 and Q = Q2. Are
Profits at a Maximum?
MC
P5
ATC
AVC
MC@Q2
Note that Price exceeds MC
When Q = Q2
Thus, marginal profits are positive
at Q2 which means that profits will
rise if more is produced
Q2
Q*
In the previous slide, ATC is minimized at
Q2. This is less than the output level that
maximizes profits
The next slide shows that if P < ATC, then
the profit maximizing level of output will be
less than the output level that minimizes
ATC
Suppose Price equals P4 and Q = Q2. Are
Profits at a Maximum?
MC
ATC
AVC
Q* Q 2
Are there any exceptions to the rule
of P=MC
• Yes, if P < AVC
• Please see the next slide. In this case,
losses are minimized by not producing at
all
Suppose P equals P1
ATC@Q*
MC
ATC
A
B
AVC
TR = E,F
P1
D
C
VC =C,D,E,F
PS = -(C,D)
F
FC =A,B
PROFIT = -(A,B,C,D)
E
Q*
Why is it in society’s interests for
producers to operate at the point
where MC = P ?
• According to the law of diminishing marginal
utility, the utility that consumers receive from a
good increases at a diminishing rate
• Based on the law of diminishing marginal returns
to labor, the total cost of producing a good can
be expected to increase at an increasing rate
Total Utility
U
Q
Total Cost
U
Q
Total Utility vs Total Cost
U
Q
Total Utility vs Total Cost
U
Please note that Utility minus
TC is maximized at Q*
Also note that the slope of the
Utility function and the total
Cost function are equal at Q*
The equality of the slopes means
That MU = MC at Q*
If MU = MC, then P = MC
Q*
Q
Question 7
Consider the nation of Atlantis which is populated
by rational perfectly informed individuals. All
markets are competitive and unregulated
Because of reduced supply due to flooding, the
price of gasoline has increased sharply.
Using consumer and producer surpluses, what is
the effect of the flood on economic welfare when
the price of gasoline is unregulated? What
happens to the profits of the gasoline
producers? Why does this happen?
Before
A,B,C,D
CS
After
A
Change
-(B,C,D)
S1
E,F
PS
W
A
P1
A,B,E
B-F
-(C,D,F)
S0
B
C
D
P0 E
A,B,C,D
E,F
B,E
F
Demand
Q1 Q
0
The change in economic welfare
Equals –(CDF) and thus society is worse
Off. Observe that producers in this
Case are better off given that area
B is larger than area F.
Question 8A
8) (A) The company known as Mississippi.com has just
reported the following financial results.
• Sales $ 14 million
• Fixed Costs $ 20 million
• Variable Costs $11 million
• profit (loss) ($17) million
• number of units sold1 million
Given that the firm’s losses exceed its revenues, the firm
has been advised to cease production. Before doing so,
the CEO of the firm wants your advice. Using the tools
of analysis presented in class, what advice would you
provide Mississippi ?
Mississipi.com
• The firm has a net loss of 17 million
• Based on its fixed costs of 20 million, the firm
would have a loss of 20 million if it closed
• Since losing 17 million is preferred to losing 20
million, the firm should stay open in the short run
• Observe that this conclusion is the result of total
revenue being larger than variable costs.
Congo.com
• B) The company known as Congo.com has just reported
the following financial results.
• Sales$ 14 million
• Fixed Costs$ 11 million
• Variable Costs $20 million
• profit (loss) ($17) million
• number of units sold1 million
• Given that the firm’s losses exceed its revenues, the firm
has been advised to cease production. Before doing so,
the CEO of the firm wants your advice. Using the tools
of analysis presented in class, what advice would you
provide Congo ?
Congo.com
• The firm has a net loss of 17 million
• Based on its fixed costs of 11 million, the firm
would have a loss of 11 million if it closed
• Since losing 11 million is preferred to losing 17
million, the firm will minimize it losses by closing
• Observe that this conclusion is the result of total
revenue being smaller than variable costs.
9) Consider the country of Atlantis. One of the key
industries in the country is the widget industry.
Because of its importance, the firm that makes
widgets is owned by the government.
The firm currently produces at the point of
diminishing marginal returns to labor.
The Laissez Faire party has proposed that the
firm be privatized. Is there any merit to this
proposal? Explain, using the tools of analysis
presented in class.
MC
Price
Point where profits are
Maximized when the
Firm is a price taker.
Also the point of
Allocative efficiency
Q0
Q*