Find the monopolists optimal price for each market p 1 and p 2 and optimal

# Find the monopolists optimal price for each market p

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Find the monopolist±s optimal price foreach market;p°1andp°2;and optimal quantity ;q°1andq°2:Also, °nd the demand elasticity for eachmarket atq°1andq°2;respectively.(e) (6 points) Consider the market for tomatoes, which are considered to be homogenous products.There are only two producers in the market. The cost functions of producer 1 and producer 2 aregiven byTC1(q1) =q1andTC2(q2) = 4q2;respectively. Let the demand function bep= 10°Q:Find the pro°t level of each producer in a Cournot-Nash equilibrium.(f) (6 points) Consider a Cournot game with homogenous products. There areN°rms in the market,andNis °xed. The demand function is given byp(Q) = 100°Qand the cost function is givenbyTC(q) = 2q:First, °nd a competitive equilibrium outcome (the market price, quantity of each°rm, and pro°t). Then, calculate the price, quantity, and pro°t in the Cournot-Nash equilibrium.What is the relationship between the competitive equilibrium outcome and the outcome in theCournot-Nash equilibrium whenNis large? 1
(g) (6 points) Consider two °rms producing a homogeneous product. Letq1andq2be the quantitiesproduced by °rm 1 and °rm 2, respectively. Demand is given byQ=52°p, whereQ=q1+q2:Thetotal cost functions of °rm 1 and °rm 2 are given byC(q1) =q1andC(q2) = 2q2;respectively.Suppose that competition is Bertrand and that each °rm has to choose its price level from a discreteset with equal intervals,P=f0;0:1;0:2; :::;9:8;9:9;10g; that is, for instance, choosingp1= 4:3isallowed but choosingp1= 0:17is not allowed.Find a Bertrand Nash equilibrium.Justify youranswer.

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• Spring '08
• Staff