Question

Consider two complementors: Firm 1 and Firm 2. Demand functions for firms 1 and 2 aregiven by

Q1¿)=1600−200P1-100P2

Q2¿)=1600−200P2-100P1

Suppose that the marginal cost functions of firms 1 and 2 are given byMC1(Q1)=MC2(Q2)=0. What price should each firm charge to maximize its profit? Showyour calculation precisely

Answer 1

Profit = TR - TC

Here MC = 0 and Fixed cost has no role to play in the decision making because it has already been incurred and is not taken into recoverable.

Profit of firm 1 is given by:

=> Profit(Pr₁) = TR₁ - TC₁ = P₁Q₁ - Q₁*MC₁ - F₁

= P₁(1600−200P₁-100P₂) - 0 - F₁ where F₁ is some fixed cost

First order condition :

d(Pr₁)/dP₁ = 0 => 1600 - 100P₂ - 400P₁ = 0

=> 4P₁ + P₂ = 16 -------------------------------(1)   

Profit of firm 2 is given by:

=> Profit(Pr₂) = TR₂ - TC₂ = P₂Q₂ - Q₂*MC₂ - F₂

= P₂(1600−200P₂-100P₁) - 0 - F₂ where F₂ is some fixed cost

First order condition :

d(Pr₂)/dP₂ = 0 => 1600 - 100P₁ - 400P₂ = 0

=> 4P₂ + P₁ = 16 -------------------------------(2)

From (1) and (2) we get : 4P₂ + P₁ = 16 = 4P₁ + P₂ => P₁ = P₂

=> 5P₁ = 5P₂ = 16 => P₁ = P₂ = 16/5 = 3.2

Hence Firm 1 should charge 3.2 and Firm should charge 3.2 in order to maximize their respective profits.