# 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.