The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following demand function for its product:
Q=120,000−10,000PQ=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.
What is the total revenue (TR) function in terms of Q?
Q−Q210,000Q−Q210,000
120,000Q−Q210,000120,000Q−Q210,000
120,000Q−10,000×Q2120,000Q−10,000×Q2
12Q−Q210,00012Q−Q210,000
What is the marginal revenue (MR) function?
1−Q5,0001−Q5,000
120,000−Q5,000120,000−Q5,000
12−Q5,00012−Q5,000
120,000−20,000Q120,000−20,000Q
What is the total cost (TC) function in terms of Q?
1.50Q21.50Q2
1.50Q1.50Q
12,000Q+1.50Q212,000Q+1.50Q2
12,000+1.50Q12,000+1.50Q
What is the marginal cost (MC) function?
1.501.50
12,000+1.50Q12,000+1.50Q
12,000+3Q12,000+3Q
3Q3Q
Which of the following is an equation for total profits (π) in terms of Q?
π=−Q210,000+10.5Q−12,000π=−Q210,000+10.5Q−12,000
π=−Q210,000+13.5Q−12,000π=−Q210,000+13.5Q−12,000
π=−Q210,000+13.5Qπ=−Q210,000+13.5Q
π=−Q210,000+10.5Qπ=−Q210,000+10.5Q
Profits are maximized when output is ?
and the price is
. Total profits at this level are
.
Points:
Close Explanation
Explanation:
What model of market pricing behavior has been assumed in this problem?
Monopoly
Pure competition

The increase in income that comes from selling one more unit of output is known as marginal revenue. Although marginal income can remain constant at a certain level of output, it will eventually start to decline as the output level rises due to the law of diminishing returns.

Q = 120,000−10,000 P

So, 10,000 P = 120,000 - Q

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

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

Total Revenue (TR) = P × Q

TR = [12 - (Q/10,000)]×Q

TR = 12Q - (Q²/10,000)

Thus, TR = 12Q - (Q²/10,000) (Option d)

MR = d(TR)/dQ

MR = 12 - (2Q/10,000)

MR = 12 - (Q/5,000)

So, MR = 12 - (Q/5,000) (Option c)

TC = Fixed Cost + Total variable cost

TC = 12,000 + 1.50Q

So, TC = 12,000+1.50Q (Option b)

MC = d(TC/dQ) = 1.50

So, MC = 1.50 (Option a)

Total profit = TR - TC

= 12Q - (Q²/10,000) - (12,000+1.50Q)

= 12Q - (Q²/10,000) - 12,000 - 1.50Q

= 10.50Q - (Q²/10,000) - 12,000

or, π = − (Q²/10,000) + 10.5Q - 12,000 (Option a)

Maximum profit:

dπ/dQ = {-2Q/10,000} + 10.5 = 0

or, - (Q/5,000) = -10.5

or, Q = 10.5 × (5,000)

or,Q = 52,500

or, Q = 52,500

P = 12 - (Q/10,000)

P = 12 - (52,500/10,000)

P = 12 - 5.25

P = 6.75

So, P = 6.75

π = - (Q²/10,000) + 10.5 Q - 12,000

π = - (52,500)²/ 10,000 + 10.5 × (52,500) - 12,000

π = -275,625 + 551,250 - 12,000

π = 263,625

So, Profit = 263,625

Monopoly because there is only one company selling a differentiated product, and P and MR are not same.

So, profit is maximized where MR = MC which is monopoly rule.

To know more about marginal revenue refer to:

https://brainly.com/question/13444663

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