Question

Question 6 (1 point) Consider a monopolist which sells output in two markets, the home market and the foreign market. The monopolist faces a linear demand curve of P1 - 20 - Q1 in the home market and P2 - 40-202 in the foreign market. The monopolists total cost is (Q=1500+q? What prices the monopolist charges in the home and the foreign market respectively? $11. $21. $12, S16 $6. $18 $18,528. none of the above

Answer 1

(6) (D)

MC = dC/dq = 2q = 2Q1 + 2Q2 [as q = Q1 + Q2]

In Home,

TR1 = P1 x Q1 = 20Q1 - Q1²

MR1 = dTR1/dQ1 = 20 - 2Q1

Setting MR1 = MC,

20 - 2Q1 = 2Q1 + 2Q2

4Q1 + 2Q2 = 20

2Q1 + Q2 = 10...........(1)

In Foreign,

TR2 = P2 x Q2 = 40Q2 - 2Q2²

MR2 = dTR2/dQ2 = 40 - 4Q2

Setting MR2 = MC,

40 - 4Q2 = 2Q1 + 2Q2

2Q1 + 6Q2 = 40.........(2)

(2) - (1) yields:

5Q2 = 30

Q2 = 6

Q1 = (10 - Q2)/2 = (10 - 6)/2 = 4/2 = 2

P1 = 20 - 2 = $18

P2 = 40 - 2 x 6 = 40 - 12 = $28

(5) (A)

P1 = 3P2, so

P2 = P1 / 3 = 0.33P1

Lerner index = - 1 / Elasticity (E) = (P - MC) / P

In market 1,

- 1 / - 1.2 = (P1 - MC) / P1

0.83 = (P1 - MC) / P1

0.83P1 = P1 - MC

MC = 0.17P1

In market 2,

- 1 / E = (P2 - MC) / P2

- 1 / E = (0.33P1 - 0.17P1) / 0.33P1

= 1 / E = 0.16P1 / 0.33P1

- 1 / E = 0.48

- E = 2.06

E = - 2.06

Since |E| > 1.2, demand is more elastic in market 2.