Question #24283

Question 8
The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following
demand function for its product:
Q = 120,000 – 10,000P
where Q is the quantity demanded per year and P is the price per lamp. The firm’s fixed
costs are $12,000 and variable costs are $1.50 per lamp.
a. Write an equation for the total revenue (TR) function in terms of Q.
[1.5 marks]
b. Specify the marginal revenue function.
[1.5 marks]
c. Write an equation for the total cost (TC) function in terms of Q.
[1.5 marks]
d. Specify the marginal cost function.
[1.5 marks]
e. Write an equation for total profits (π) in terms of Q. At what level of output (Q) are
total profits maximised? What price will be charged? What are total profits at this
output level?
[2 marks]
f. Check your answer in Part (e) by equating the marginal revenue and marginal
cost functions, determined in Parts (b) and (d), and solving for Q.
[2 marks]
g. What model of market pricing behavior has been assumed in this problem?
Explain

Expert's answer

Question 8

The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following demand function for its product:

Q = 120,000 – 10,000P, where Q is the quantity demanded per year and P is the price per lamp. The firm’s fixed

costs are $12,000 and variable costs are $1.50 per lamp.

a. Write an equation for the total revenue (TR) function in terms of Q.

P = (120,000 - Q)/10,000 = 12 - Q/10,000

TR = P*Q = 12Q - Q^2/10,000

b. Specify the marginal revenue function.

MR = TR' = 12 - Q/5,000

c. Write an equation for the total cost (TC) function in terms of Q.

TC = 12,000 + 1.5Q

d. Specify the marginal cost function.

MC = TC' = 1.5

e. Write an equation for total profits (π) in terms of Q. At what level of output (Q) are total profits maximized?

What price will be charged? What are total profits at this output level?

π = TR - TC = 12Q - Q^2/10,000 - 12,000 - 1.5Q = 10.5Q - Q^2/10,000 - 12,000

MR = MC = P = 1.5, if it is perfect competitive market.

P = 12 - Q/10,000 = 1.5

Q/10,000 = 10.5

Q = 105,000

π = TR - TC = 1.5*105,000 - 12,000 - 1.5*105,000 = -12,000

So, P = AVC, it is the minimal point, where the firm can produce.

f. Check your answer in Part (e) by equating the marginal revenue and marginal

cost functions, determined in Parts (b) and (d), and solving for Q.

MR = MC

12 - Q/5,000 = 1.5

Q/5,000 = 10.5

Q = 52,500

First calculations for Q get another answer, so MR = MC not equal P. So, it is monopolistic market.

π = TR - TC = 10.5Q - Q^2/10,000 - 12,000 = $263,625

P = 12 - Q/10,000 = $6.75

g. What model of market pricing behavior has been assumed in this problem?

Explain

So, monopolistic model of pricing was assumed, because P = 6.75 is greater than MR = MC = 1.5.

The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following demand function for its product:

Q = 120,000 – 10,000P, where Q is the quantity demanded per year and P is the price per lamp. The firm’s fixed

costs are $12,000 and variable costs are $1.50 per lamp.

a. Write an equation for the total revenue (TR) function in terms of Q.

P = (120,000 - Q)/10,000 = 12 - Q/10,000

TR = P*Q = 12Q - Q^2/10,000

b. Specify the marginal revenue function.

MR = TR' = 12 - Q/5,000

c. Write an equation for the total cost (TC) function in terms of Q.

TC = 12,000 + 1.5Q

d. Specify the marginal cost function.

MC = TC' = 1.5

e. Write an equation for total profits (π) in terms of Q. At what level of output (Q) are total profits maximized?

What price will be charged? What are total profits at this output level?

π = TR - TC = 12Q - Q^2/10,000 - 12,000 - 1.5Q = 10.5Q - Q^2/10,000 - 12,000

MR = MC = P = 1.5, if it is perfect competitive market.

P = 12 - Q/10,000 = 1.5

Q/10,000 = 10.5

Q = 105,000

π = TR - TC = 1.5*105,000 - 12,000 - 1.5*105,000 = -12,000

So, P = AVC, it is the minimal point, where the firm can produce.

f. Check your answer in Part (e) by equating the marginal revenue and marginal

cost functions, determined in Parts (b) and (d), and solving for Q.

MR = MC

12 - Q/5,000 = 1.5

Q/5,000 = 10.5

Q = 52,500

First calculations for Q get another answer, so MR = MC not equal P. So, it is monopolistic market.

π = TR - TC = 10.5Q - Q^2/10,000 - 12,000 = $263,625

P = 12 - Q/10,000 = $6.75

g. What model of market pricing behavior has been assumed in this problem?

Explain

So, monopolistic model of pricing was assumed, because P = 6.75 is greater than MR = MC = 1.5.

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