Question

The market demand curve of a local pizza is QD= 100 − 4P. The total cost curve of Pat’s Pizza Kitchen is TC = 0.5Q2 + Q+5. Assuming Pat’s Pizza is doing business in a competitive industry and the price of the pizza is $10 for all firms. Using Excel to calculate the firm’s total revenue, total cost, and profit for q = 1 to q = 25 in increments of 1. (Note: your answers should be rounding decimals to the nearest whole number. Example: 12.3 => 12, 15.7=> 16):

At the price $10, how many units of output will the entire industry produce? ________ How many units of output will Pat’s Pizza produce to maximize profits (or minimize loss) in the short run? ________

Now, the industry turns into a monopoly.

Assuming the marginal cost curve stays the same as before. What is the profit-maximizing level of output? _________ What is total profit for the monopolist? ________ What is the price of the good the monopolist charges? ______ .

Answer 1

output (q)	Price	Total Revenue	Total Cost	Profit
1	10	10	6.5	3.5
2	10	20	9	11
3	10	30	12.5	17.5
4	10	40	17	23
5	10	50	22.5	27.5
6	10	60	29	31
7	10	70	36.5	33.5
8	10	80	45	35
9	10	90	54.5	35.5
10	10	100	65	35
11	10	110	76.5	33.5
12	10	120	89	31
13	10	130	102.5	27.5
14	10	140	117	23
15	10	150	132.5	17.5
16	10	160	149	11
17	10	170	166.5	3.5
18	10	180	185	-5
19	10	190	204.5	-14.5
20	10	200	225	-25
21	10	210	246.5	-36.5
22	10	220	269	-49
23	10	230	292.5	-62.5
24	10	240	317	-77
25	10	250	342.5	-92.5

QD = 100 - 4P

QD = 100 - 4(10)

QD = 100 - 40

QD = 60.

At the price $10, 60 units of output will the entire industry produce.

9 units of output will be produce to maximize the profit by Pat's Pizza.

Monopoly

TC = 0.5Q^2 + Q +5

MC = 0.5 (2)Q + 1.

MC = Q +1

Q = 100 - 4P

4P = 100 - Q

P = (100 -Q)/4

P = 25 - 0.25Q

TR = P Q

TR= (25 - 0.25Q) Q

TR = 25Q - 0.25Q^2

MR = 25 - 0.5Q

At equilibrium point, MR = MC

25 - 0.5Q = Q + 1

25 - 1 = Q + 0.5Q

24 = 1.5Q

Q = 24 / 1.5

Q = 16

P = 25 - 0.25Q

P = 25 - 0.25 (16)

P = 25 - 4

P = 21

Profit = TR - TC

Profit = P*Q - (0.5Q^2 + Q + 5)

Profit = (21) (16) - (0.5 (16)^2 + 16 + 5)

Profit = 336 - 149.

Profit = 187

The profit maximizing level of output is 16.

The total profit of monopolist is 187.

The price charged by the monopolist is 21.