Question

4. A monopolist produces a product with a constant marginal cost equal to $400 per unit and a fixed cost of $80000. The demand for the product is Q= 500-0.5*P. The monopolist’s maximal profits are equal to

   1. a) $0.00

   2. b) $5000.00

   3. c) $45000.00

   4. d) None of the above.

Answer 1

For a monopolist, the demand curve is given as

Q = 500 - 0.5P

=> 0.5P = 500 - Q

=> P = 1000 - 2Q

Total Revenue = Price * Quantity = (1000 - 2Q) * Q = 1000Q - 2Q^2

Marginal Revenue, MR = d/dQ (Total Revenue) = d/dQ (1000Q - 2Q^2) = 1000 - 2 * 2Q = 1000 - 4Q

Marginal Cost, MC = $400

Profit maximizing quantity is the quantity at which MR = MC

=> 1000 - 4Q = 400

=> 4Q = 1000 - 400

=> Q = 600/4

=> Q = 150

When Q = 150, Total Cost = Fixed Cost + MC * Quantity (As the marginal cost is constant)

Total Cost = $80,000 + $400*150 = $140,000

Total Revenue = 1000Q - 2Q^2 = 1000*150 - 2*150^2 = $105,000

Profit(Loss) = Total revenue - Total Cost = $105,000 - $140,000 = -$35,000(loss)

The monopoly can never earn profits and its minimum loss = $35,000

Ans: d. None of the above

Price	Quanttiy	TR	MR	MC	TC	ATC
1000	0	0	-	-	480000	-
900	50	45000	900	400	440000	8800.00
800	100	80000	700	400	400000	4000.00
700	150	105000	500	400	360000	2400.00
600	200	120000	300	400	320000	1600.00
500	250	125000	100	400	280000	1120.00
400	300	120000	-100	400	240000	800.00
300	350	105000	-300	400	200000	571.43
200	400	80000	-500	400	160000	400.00
100	450	45000	-700	400	120000	266.67
0	500	0	-900	400	80000	160.00

From the above table, it can be observed that the price is always less than the ATC. Hence, the firm can never earn profit.