Question

The market consists of 2 firms. The firms produce the same product. Firm 1 with $1 per-unit cost (C₁(q₁)=1q₁). Firm 2 with $1 per-unit cost (C₂(q₂)=1q₂). Firm 1 can produce 2 or 4 or 6 units. Firm 2 can produce 2 or 4 or 6 units. The industry's demand function is Q = 50 - P (P=price, Q=total quantities). The firms choose their quantities simultaneously.

1a) Find Firm 1's optimal production levels. q1=?

1b) Find Firm 2's optimal production levels. q2=?

1c) Determine the equilibrium price. p=?

1d) Firm 1 will earn how much?

1e) Firm 2 will earn how much?

Answer 1

A) The MAXIMUM they can produce=6

So Q1=6-0.5q2{ best response function of firm 1}

Q2=6-0.5q1{ best response function of firm 2}

Q2=6-0.5(6-0.5q2){ putting Q1 into q2}

Q2=3/0.75=4

Q1=6-0.5*4=4

Option B is correct

B) option B is correct

C) Q1+q2=4+4=8

P=50-8=42

Option C is right

D) Profit of firm 1=(42-1)*4=41*4=164

OPTION B is correct

E) Profit of firm 2=( 42-1)*4=164

OPTION B is correct