Econ302
Homework Assignment 6
Solution
1.
How can a firm determine an optimal twopart tariff if it has two customers with
different demand curves?
(Assume that it knows the demand curves.)
If all customers had the same demand curve, the firm would set a price equal
to marginal cost and a fee equal to consumer surplus.
When consumers have
different demand curves and, therefore, different levels of consumer surplus,
the firm is faced with the following problem.
If it sets the user fee equal to the
larger consumer surplus, the firm will earn profits only from the consumers
with the larger consumer surplus because the second group of consumers will
not purchase any of the good.
On the other hand, if the firm sets the fee equal
to the smaller consumer surplus, the firm will earn revenues from both types of
consumers.
2.
Elizabeth Airlines (EA) flies only one route: ChicagoHonolulu.
The demand for
each flight on this route is Q = 500 
P.
Elizabeth’s cost of running each flight is
$30,000 plus $100 per passenger.
a.
What is the profitmaximizing price EA will charge?
How many people will
be on each flight?
What is EA’s profit for each flight?
To find the profitmaximizing price, first find the demand curve in inverse
form:
P
= 500 
Q
.
We know that the marginal revenue curve for a linear demand curve will have
twice the slope, or
MR
= 500  2
Q
.
The marginal cost of carrying one more passenger is $100, so
MC
= 100.
Setting marginal revenue equal to marginal cost to determine the profit
maximizing quantity, we have:
500  2
Q
= 100, or
Q
= 200 people per flight.
Substituting
Q
equals 200 into the demand equation to find the profit
maximizing price for each ticket,
P
= 500  200, or
P
= $300.
Profit equals total revenue minus total costs,
= (300)(200)  {30,000 + (200)(100)} = $10,000.
Therefore, profit is $10,000 per flight.
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b.
Elizabeth learns that the fixed costs per flight are in fact $41,000 instead of
$30,000.
Will she stay in this business long?
Illustrate your answer using a
graph of the dema
nd curve that EA faces, EA’s average cost curve when fixed
costs are $30,000, and EA’s average cost curve when fixed costs are $41,000.
An increase in fixed costs will not change the profitmaximizing price and
quantity. If the fixed cost per flight is $41,000, EA will lose $1,000 on each
flight.
The revenue generated, $60,000, would now be less than total cost,
$61,000.
Elizabeth would shut down as soon as the fixed cost of $41,000 came
due.
300
500
200
250
300
305
400
500
Q
P
D
AC
1
AC
2
Figure 11.6.b
c.
Wait!
EA finds out that two different types of people fly to Honolulu.
Type A
is business people with a demand of Q
A
= 260  0.4P. Type B is students whose
total demand is Q
B
= 240  0.6P.
The students are easy to spot, so EA decides
to charge them different prices. Graph each of these demand curves and
their horizontal sum.
What price does EA charge the students?
What price
does EA charge other customers?
How many of each type are on each flight?
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 Spring '08
 TOOSSI
 Consumer Surplus, Supply And Demand, ea

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