Question

Assume:

a.     Market demand:  P = 100 -.5Q₁ - .5 Q₂

b.    TC₁ = 4Q₁   and TC₂ = .25Q₂²

Make sure you show me all of your computations (TR, TC, and your partial derivatives).

You will be using the same data for the Cournot and Cartel problem.  Find the quantities for both firms in both market types that maxes profit.  As a stretch question how much profit does each Cournot firm make and what is the joint profit for the cartel.

Answer 1

1) Cournot competition is choosing simoultaneous quantity model.

profit (П₁) = total revenue (P.Q₁) - total cost (TC₁)

П₁= (100- 0.5Q₁- 0.5Q₂)Q₁ - 4Q₁ .............(1)

similarly, П₂ = (100- 0.5Q₁- 0.5Q₂)Q₂ - 0.25Q₂² ...............(2)

Partial differentiating equation (1) w.r.t Q₁ and equation (2) w.r.t Q₂ we get as follows:

2) now for cartel both firm will collude and want to maximise the joint profit as follows:

max П (Q₁, Q₂) = P.(Q₁+Q₂) - TC₁ - TC₂

we get;