Question

A firm has two plants and wishes to maximize profits. The
marginal cost curves for the two plants are: MC_{1} =
2Q_{1} and MC_{2} = 3Q_{2}. 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.

Answer #1

MC1 = 2Q1 and MC2 = 3Q2

The demand is P = 100 - 0.4Q

For MR:

Calculate TR= P*Q= 100-0.4Q2

Differentiate TR with respect to Q to calculate MR

MR=100-0.8Q= 100-0.8Q1-0.8Q2

Maximizing profit condition:

For plant 1: MR=MC1

100-0.8Q1-0.8Q2=2Q1

2.8Q1+0.8Q2=100 Equation 1

For plant 2:

100-0.8Q1-0.8Q2=3Q2

0.8Q1+3.8Q2=100 Equation 2

Solve equation 1 and 2:

Multiply 0.8 in equation 1 and 2.8 in equation 2 and then subtract them:

2.24Q1+0.64Q2-2.24Q1-10.64Q2= 80-280

-10Q2= -200

Q2= 20

Put Q2=20 in equation 1:

2.8Q1+0.8(20)=100

2.8Q1= 84

Q1= 30

**Correct answer is D. Q = 30; 20.**

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
= Q1 + Q2. The marginal costs associated with
producing in the two plants are MC1 = 2Q1 and
MC2 = 4Q2.
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...

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?

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...

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 maximum profit? Assume total Fixed Costs
for plant 1 (TFC1) = $0 and Total Fixed Costs for plant
2 (TFC2) = $0.

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

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.

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?

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?

Suppose there is a perfectly competitive industry in Dubai,
where all the firms are identical. All the firms in the industry
sell their products at 20 AED. The market demand for this product
is given by the equation: (Total marks = 5)
Q = 25 – 0.25P
Furthermore, suppose that a
representative firm’s total cost is given by the equation:
TC = 50 +4Q +
2Q2
What is the inverse demand function for this market?
Calculate the MC function?
Calculate...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 24 minutes ago

asked 24 minutes ago

asked 42 minutes ago

asked 44 minutes ago

asked 47 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago