Question

GAME THEORY:

Two countries produce oil. The per unit production cost of Country 1 is C1 = $2 and of country 2 it is C2 = $4. The total demand for oil is Q = 40-p where p is the market price of a unit of oil. Each country can only produce either 5 units, 10 units or 15 units. The total production of the two countries in a Nash equilibrium is:

A. 10

B. 15

C. 20

D. 25

E. 30

Please show all work and explain! Thank you!

Answer 1

			Firm 2
		5	10	15
	5	( 140, 130)	( 115, 210)	( 90, 240)
Firm 1	10	( 230, 105)	( 180, 160)	( 130, 165)
	15	( 270, 80)	( 195, 110)	( 120, 90)

If both produce 5 units each then we can calculate price in the market P = 30. At price = 30 profit to country 1 = (30-2)*5 = 140 and to country 2 will be (30-4)*5 = 130

Similarly we can calculate the profit level for each level of production by each firm.

We will find the best response of each firm

Firm 1

BR1( Q2 = 5) = 15

BR1( Q2 = 10) = 15

BR1( Q2 = 15) = 10

Firm 2

BR2( Q1 = 5) = 15

BR2( Q1 = 10) = 15

BR2( Q1 = 15) = 10

The nash equilibrium is the mutual best response. So firms will produce Q1 =10 Q2 =15 or Q1 = 15 or Q2 = 10. Therefore Total output produce dwill be 25.

The correct option is D