Question

Questions 18-19 refer to the following: There 2 firms in a Cournot Oligopoly market for cell phone service in a Texas county. The market inverse demand function and the total cost functions each of the two firms are as follows: P = 50 – 0.25(Q1 + Q2) (market inverse demand) TC1 = 5 + 10Q1 (total cost function for firm 1) TC2 = 2 + 12Q2 (total cost function for firm 2) 18. Which of the following represents the equilibrium market price, and level of output for firm 1 and firm 2?

a. P = $35 Q1 = 42 Q2 = 42

b. P = $24 Q1 = 56 Q2 = 48

c. P = $24 Q1 = 48 Q2 = 56

d. P = $24 Q1 = 52 Q2 = 52

e. P = $28 Q1 = 36 Q2 = 32

In equilibrium, what will the firm 2 profit equal?

a. 2 = $240

b. 2 = $350

c. 2 = $574

d. 2 = $779

e. 2 = $1,152

Answer 1

# P250 -0.25 1Q, +Q2) TC, a 5 + 100, TC2, 2 + 1202 Profit T frenction of firm & can be giver lag PQ – TC, 2 0 [50-0.25 (Q, +2₂) 7Q - [5 + 100,] - 50Q, – 0.25 Q,² – 0.25 Q Q - 5 - 100, T & 400- 0.25 0 ² - 0.25 Q, Q₂ - 5 first order condition can be given by da, a ? 40 - 0,5 , -0.25Q, = 0 0.5Q, +0.25 Q2 = 40 -> 20, + ,160 ... ☺ Profit function of firm e can be given by Te PQ, - TC2 [ 50 -0.25 (Q1 +8₂) JQ₂ - [2 + 12 Q7 1, 2 38 , -0,25 9, Q, - 0.250- 2 first order condition can lee given by. 38 -0.250,- 0.5Q2 = 0 Scanned with CamScanner =) 0.250, +0.450,- 38

Q. + LQ, - 152 Q,2 152-2Q2 By putting above equation in equation © We will get * 2 [152 - 2003 + Q, 2160 3Q2 = 144 Q2 248 Q, 2. 152-d(48) 256 ( Q, 256 ; Q2 248 P. 50 - 0,25 (56+48) loption D is correct cs Scanned with CamScanner

# Since Profit of firm 2 is given by To 2380 -0.25 (6, 76,) - 0.95 Q 2 ² - 2 722 5747 I option ② is correct CS Scanned wi CamScanner