Question

Exercise 11.3 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

Answer 1

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

Total Revenue (TR) = P*Q = [12 - (Q/10,000)]*Q = 12Q - (Q²/10,000)

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

MR = d(TR)/dQ = 12 - (2Q/10,000) = 12 - (Q/5,000)

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

TC = Fixed Cost + Total variable cost = 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

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

Maximum profit:
So, -(Q/5,000) = -10.5
So, Q = 10.5*(5,000) = 52,500
So, Q = 52,500

P = 12 - (Q/10,000) = P = 12 - (52,500/10,000) = 12 - 5.25 = 6.75
So, P = 6.75

π = −(Q²/10,000)+10.5Q−12,000 = -(52,500)²/10,000 + 10.5(52,500) - 12,000 = -275,625 + 551,250 - 12,000 = 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.