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transfer price

Please answer the questions below and give full explanations so I can follow and learn how to apply myelf.

1. You are the manager of a firm that sells its product in a competitive market at a price
of $60. Your firm's cost function is C(Q) = 30 + 3Q2.
a. What is the profit-maximizing output for your firm?
b. What is the maximum profit for your firm?

2. You are the manager of a monopoly that faces a demand curve described by
P = 85 - 5Q. Your costs are C(Q) = 20 + 5Q.
a. What is the profit-maximizing output?
b. What is the profit-maximizing price?)
c. What is the maximum profit? (

3. A monopoly has two production plants with cost functions C1(Q1) = 50 + 0.1 Q12 and
C2(Q2) = 30 + 0.05 Q22. The demand it faces is Q = 500 - 10 P.
a. What is the profit-maximizing level of output? ;

b. What is the profit-maximizing price? (
c. What is the maximum profit? (Answer: Not given)

4. Consider the following pay-off table for a one-shot game:

Firm A
`
Firm B

Low Price

High Price

Low Price

(2, 2)
(10, -8)

High Price

(-8, 10)
(15, 15)

a. What are the dominant strategies for Firm A and Firm B, respectively?
(Answer: .)
b. What are the Nash equilibrium strategies for this game?
[Answer:
5. You are the manager of a Mom and Pop store that can buy milk from a supplier at
$3.00 per gallon. Suppose the elasticity of demand for milk by customers at your store
is -4.
a. What is the profit-maximizing price for the milk you sell?

6. During spring break, students have an elasticity of demand for a trip to Cancun
Mexico of -4. Assume the general public has an elasticity of -2.
a. How much should an airline charge students for a ticket if the price it charges
the general public is $420?

7. The average consumer at a firm with market power has an inverse demand function of
P = 10 - Q. The firm's cost function is C(Q) = 2Q. If the firm engages in two part
pricing,
a. what is the optimal fixed fee to charge each consumer?
b. what is the optimal price to charge a consumer for each unit purchased?
()

8. A firm with market power has an individual consumer demand of Q = 4 - 0.25P and
costs of C(Q) = 8Q.
a. What is optimal price to charge for a block of 2 units?

9. Suppose two types of consumers buy pants and shirts. Consumers of type A will pay
$70 for pants and $20 for a shirt. Consumers of type B will pay $60 for pants and $25
for a shirt. The firm selling suits faces no competition and has a marginal cost of zero
and cannot price discriminate between the consumers.
a. What is the optimal commodity bundling strategy? (

10. A firm has a division that produces X, whose total costs are C(Q) = 10 + 5Q2 (where
Q is the quantity of X). The marketing division adds its own total costs of 5 + 3Q.
There is no external market price of X.
a. What should be the transfer price of X?)

Solution Preview

1. You are the manager of a firm that sells its product in a competitive market at a price of $60. Your firm's cost function is C(Q) = 30 + 3Q2.
a. What is the profit-maximizing output for your firm?

The marginal cost is MC = dC/dQ = 6Q
By first order condition, the firm will max profit by setting MC = MR = P in a competitive market, i.e.,
6Q = 60
Q = 60/6 = 10
So the profit-maximizing output is 10.

b. What is the maximum profit for your firm?

max Profit = P*Q - C
= 60*10 - (30 + 3*10^2) = $270

2. You are the manager of a monopoly that faces a demand curve described by
P = 85 - 5Q. Your costs are C(Q) = 20 + 5Q.

a. What is the profit-maximizing output?

The firm's total revenue is TR = P*Q= (85 - 5Q)*Q = 85Q - 5Q^2
so it's marginal revenue is MR = dTR / dQ = 85 - 10Q
Also, the firm's marginal cost is MC = dC/dQ = 5
The monopolist will max profit by setting MC = MR, i.e.,
85 - 10Q = 5
80 = 10Q
Q = 8

b. What is the profit-maximizing price?)
from the demand curve:
P = 85 - 5Q = 85 - 5*8 = $45

c. What is the maximum profit?

max Profit = P*Q - C
= 45*8 - (20 + 5*8) = $300

3. A monopoly has two production plants with cost functions C1(Q1) = 50 + 0.1 Q1^2 and C2(Q2) = 30 + 0.05 Q2^2. The demand it faces is Q = 500 - 10 P.

a. What is the profit-maximizing level of output? ;

MC1 = dC1/dQ1 = 0.2 Q1
MC2 = dC2/dQ2 = 0.1 Q2
From demand curve, we rewrite it into: P = 50 - 0.1 Q
Then firm's total revenue is
TR = P*Q= (50 - 0.1Q)*Q = 50Q - 0.1Q^2
it's marginal revenue is
MR = dTR / dQ = 50 - 0.2 Q
Also we know Q= Q1 + Q2, then
MR = dTR / dQ = 50 - 0.2 (Q1+Q2)

The ...

Solution Summary

Determine transfer price and other factors.

$2.19