Two firms produce and sell differentiated products that are substitutes for each

Question

Two firms produce and sell differentiated products that are substitutes for each other. Their demand curves are

Firm 1:

Upper Q1=403P 1+P2

Firm 2:

Upper Q 2=403P 2+P1

Both firms have constant marginal costs of

$4.9 per unit.

Both firms set their own price and take their competitor's price as fixed. Use the Nash equilibrium concept to determine the equilibrium set of prices. Since the firms areidentical, they will set the same prices and produce the same quantities.

In equilibrium, each firm will charge a price of ????????

and produce ???? units of output. (Enter your responses rounded to two decimal places.)

Each firm will earn a profit of ?????(Enter your response rounded to two decimal places.)

Explanation / Answer

Pr1 = Profit (firm 1) = P1 x Q1 - 4.9 x Q1

Pr1 = 40P1 -3P12 + P2P1 -4.9 x (40 - 3P1 + P2)

Profit would be maximized when d(Pr1)/dP1 = 0:

40 - 6P1 + P2 +14.7 = 0

6P1 - P2 = 54.7

Similarly for firm 2:

Pr2 = 40P2 -3P22 + P2P1 -4.9 x (40 - 3P2 + P1)

Profit would be maximized where d(Pr2)/dP2 = 0:

6P2 - P1 = 54.7

Using the equations given above:

P2 = P1 = $10.94

Q2 = Q1 = 18.12

Profit = (10.94 - 4.9) x 18.12 = $109.4

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