Question

Monopolistic firm faces the inverse demand function p = 250 – 6Q. Firm’s total cost of production is C = 1250 + 10Q + 8Q² :

1. Create a spreadsheet for Q = 1 to Q = 20 in increments of 1. Determine the profit-maximizing output and price for the firm and the consequent level of profit.

2. Will the firm continue the production at the profit-maximizing level of output? Show why or why not?

3. Calculate the Lerner Index of monopoly power for each output level and verify its relationship with the value of the price elasticity of demand at the profit-maximizing level of output.

4. Suppose that a specific tax of 10 per unit is imposed on the monopoly. What is the effect on the monopoly’s profit-maximizing price?

Answer 1

1) The table is drawn below. The profit-maximizing/loss minimizing output is 9 units and price for the firm is 196 and the consequent level of loss = -224

Q	Demand(P)	TR	TC	Profit
1	244	244	1268	-1024
2	238	476	1302	-826
3	232	696	1352	-656
4	226	904	1418	-514
5	220	1100	1500	-400
6	214	1284	1598	-314
7	208	1456	1712	-256
8	202	1616	1842	-226
9	196	1764	1988	-224
10	190	1900	2150	-250
11	184	2024	2328	-304
12	178	2136	2522	-386
13	172	2236	2732	-496
14	166	2324	2958	-634
15	160	2400	3200	-800
16	154	2464	3458	-994
17	148	2516	3732	-1216
18	142	2556	4022	-1466
19	136	2584	4328	-1744
20	130	2600	4650	-2050

Firm is consistently making losses. But if it leaves the market it will still be paying a cost of 1250 as it is a fixed cost. Hence current loss is less than the loss of 1250 so it will produce.

Lerner index = P - MC/P,. Here MC = 10 + 16Q = 10 + 16*9 = 154 . At the current level, price is 196 so lerner index = (196 - 154)/196 = 0.2143

Elasticity = 1/L = 1/0.2143 = 4.6667

When a tax is imposed, MC becomes = 10 + 16Q + 10 = 20 + 16Q. New combination of price and quantity is

20 + 16Q = 250 - 12Q

28Q = 230

Q = 8.21 and price = 201. Hence price will be higher.