Answer 2.2. Let pl(r) be the market price of the good when the output is Y, c(yi)is the cost of firm i when its output is i. The two firms have the same cost function. The cartel maximizes their total profit max Ti= P(y1+y2)(91+y2)-c(y1)-c(u2) The FOcs are p(Y)+p(Y*)Y=c() We look for a solution for which yi= y*(the symmetric solution). Thus, the FOC P(Y)+P(YY=c We can rewrite(2) as MR(Y)=C where R(Y=P(YY. On the other hand, the Cournot output is determined by MR(Y*)-SP(Yr=c D Figure 5. 1. A market-share Cournot equilibrium In the diagram, point A is the 'competitive solution,, for which each firm takes the market price as given; point B is our solution, for which each firm acts upon a decreas demand and assume equal market share as the others reaction; point C is the Cournot librium From the diagram we can conclude that 2-6Answer 2.2. Let p(Y ) be the market price of the good when the output is Y, c(yi) is the cost of firm i when its output is yi. The two firms have the same cost function. The cartel maximizes their total profit: max y1, y2 πi ≡ p(y1 + y2)(y1 + y2) − c(y1) − c(y2). The FOCs are p(Y ∗ ) + p0 (Y ∗ )Y ∗ = c0 (y∗ i). (1) We look for a solution for which y∗ 1 = y∗ 2 (the symmetric solution). Thus, the FOC becomes p(Y ∗ ) + p0 (Y ∗ )Y ∗ = c0 Y ∗ 2  . (2) We can rewrite (2) as MR(Y ∗ ) = c0 Y ∗ 2  , where R(Y ) ≡ p(Y )Y. On the other hand, the Cournot output is determined by MR(Y ∗ ) − 1 2 p0 (Y ∗ )Y ∗ = c0 Y ∗ 2  . . ps5-1 p Y B A MR(Y ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2 ' Y c D MR(Y ) 2 p'(Y )Y 1 − . C . Figure 5.1. A market-share Cournot equilibrium In the diagram, point A is the ‘competitive solution’, for which each firm takes the market price as given; point B is our solution, for which each firm acts upon a decreasing demand and assume equal market share as the other’s reaction; point C is the Cournot equilibrium. From the diagram, we can conclude that 2—6