Question

You are the manager of a firm that produces output in two
plants. The demand for your firm's product is P = 120 − 6Q, where Q
= Q_{1} + Q_{2}. The marginal costs associated with
producing in the two plants are MC_{1} = 2Q_{1} and
MC_{2} = 4Q_{2}.

Please explain and show all steps in deriving the answers, thank you!

a. How much output should be produced in plant 1 in order to maximize profits? Answer: 6

b. What price should be charged to maximize profits? Answer: 66

c. What price should be charged in order to maximize revenues? Answer: 60

Answer #1

You are the manager of a firm that produces output in two
plants. The demand for your firm's product is P = 78 − 15Q, where Q
= Q1 + Q2. The marginal costs associated with
producing in the two plants are MC1 = 3Q1 and
MC2 = 2Q2.
a. How much output should be produced in plant 1 and plant 2 in
order to maximize profits? 1 and 1.5 units respectively
b. What price should be charged to maximize...

Manager of firm that produces output in two
plants.
The demand for your firm’s product is P = 80 – Q, where
Q = Q1 + Q2.
The marginal cost associated with producing in the two
plants are MC1 = Q1 and MC2 = 8.
What is the profit maximizing price that the firm should
charge?

Rexburg Technologies operates two plants. The demand
equation for Rexburg's product is P = 38 – 2.5Q, where Q is in
thousands of units. The marginal cost of production in the two
plants are MC1 = 2Q1 and MC2 = 4Q2, respectively. To maximize
profits, Rexburg should charge a price of:
23.00.
$32.50.
$8.00.
$10.75.
None of the options

A firm has two plants and wishes to maximize profits. The
marginal cost curves for the two plants are: MC1 =
2Q1 and MC2 = 3Q2. The demand is P
= 100 - .4Q. To maximize profits, how much output should be
produced in plant#1 and plant#2, respectively?
A. Q = 40;10.
B. Q = 10; 40.
C. Q = 20; 30.
D. Q = 30; 20.
E. None of the above.

Suppose the inverse demand for a monopolist’s product is given
by
P (Q) = 20 – 3Q
The monopolist can produce output in
two plants. The marginal cost of producing in plant 1 is
MC1 = 20 +
2Q1
While the marginal cost of producing
in plant 2 is
MC2 = 10 +
5Q2
How much output should be produced in each plant?
What price should be charged?

Suppose the inverse demand for a monopolist’s product is given
by
P (Q) = 20 –
3Q
(Total marks = 5)
The monopolist can produce output in
two plants. The marginal cost of producing in plant 1 is
MC1 = 20 +
2Q1
While the marginal cost of producing
in plant 2 is
MC2 = 10 +
5Q2
How much output should be produced in each plant?
What price should be charged?

Multiplant monopoly problem: Assume the firm has two plants
with the following marginal cost functions:
MC1= 20 +
2Q1
MC2= 10 +
5Q2
What is the profit maximizing
price? Show your work.

1. A monopolist producer of a sailboat motor sells
output in two geographically separated markets (East and West
Coasts). Inverse demand and marginal revenue for the two
markets are:
P1 = 2000 - Q1 and MR1 = 2000 - 2Q1 and P2 = 3000 -
2Q2 and MR2 = 3000 - 4Q2.
The monopolist’s total cost is C = 500,000 + 1000(Q1 +
Q2). What are price, output, profits, marginal revenues, and
deadweight loss for the following two cases:
(a)...

Multiplant monopoly problem: Assume
the firm has two plants with the following marginal cost
functions:
MC1
= 20 +
2Q1
MC2
= 10 +
5Q2
Assume that the
inverse demand curve is P = 500-Q.
What is the
profit maximizing outputs produced in each plant? Show your
work.
What is the
profit maximizing price? Show your work.
What is the
maximum profit?

Suppose there are two firms in a market who each simultaneously
choose a quantity. Firm 1’s quantity is q1, and firm 2’s
quantity is q2. Therefore the market quantity is Q =
q1 + q2. The market demand curve is given by
P = 160 - 2Q. Also, each firm has constant marginal cost equal to
10. There are no fixed costs.
The marginal revenue of the two firms are given by:
MR1 = 160 – 4q1 – 2q2
MR2...

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