Question

There are only two luxury electric car producers in Carmania, Firm 1 and Firm 2. The cars they produce are essentially identical. The market inverse demand function for luxury electric cars in Carmania is given by P = a – bQ, where P is price (in thousands euros); Q market output (in number of cars); and a and b are parameters. Competition in the Carmania auto market works as follows: At the beginning of each year, both firms simultaneously and independently decide how many cars to produce. Market price is then determined by total demand and total supply. Marginal cost (in thousands euros) is given by 77 for Firm 1 and 74 for Firm 2. Currently, Firms 1 and 2 are producing 170 and 200, respectively, whereas the market price is 94. Find the parameters a and b in the market inverse demand function. Determine equilibrium profit of each firm, as well as consumer's surplus and social

Answer 1

q1+q2 = 170+200 = 370

P = 94

SO, 94 = a - 370b ......(1)

as two Firms play cournot game

Then, π1 = (P-77)q1

= (a- bq1 - bq2-77)q1

= (a - 77 - bq2)q1 - bq1^{​​​​2}

FINDING best Response function

BR1 : dπ1/dq1 = 0

(a-77-bq2) = 2bq1

Then, (a-77-200b) = 340b

a- 77 = 540b .....(2)

Solving two equations

b = .1 , a= 131

.

π1= (P-MC1)*q1

= (94-77)*170

= 2890

π2 = (94-74)*200

= 20*200

= 4,000

.

CS = .5*(131-94)*(200+170)

= .5*37*370

= 6845

.

Social Surplus = CS + π

= 6845 + (4000+2890)

= 6845 + 6890

= 13,735