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 set its price to 2 or 3 or 4 $. Firm 2 can set its price to 2 or 3 or 4 $. The industry's demand function is Q= 10 – P (P-price, Q- total quantities). The firms choose their quantities simultaneously.

1a) Find Firm 1 optimal price P1=?

1b) Find Firm 2 optimal optimal price   p2=?.

1c) Determine the equilibrium quantity? (Q=?)

1d) Firm 1 will earn? (pi1=?)

1e) Firm 2 will earn? (pi2=?)

Answer 1

At eqm,

Both Firms will be involved in price war,

If By Firm charges a price , which is a bit lower than the price of Other Firm, it will capture the entire market,

Seeing this , other Firm will also deviate, & want to reduce the price, so as to capture entire market

Thus at eqm, both will settle prices, so that no one has incentive to deviate , which is when both charge P = 2

1a) P1* = 2

1b) P2*= 2

1c) Q*= 10-2= 8

1d) π1 = (P-MC)q1

Both produce half of total market Output = 4

π1= (2-1)*4 = 4

1e) π2= (2-1)*4 = 4