1. (30 points) Consider a market with two firms. Market Demand is given by P-100
ID: 1173984 • Letter: 1
Question
1. (30 points) Consider a market with two firms. Market Demand is given by P-100-Q. Firm A has a constant marginal cost of 10 and Firm B has a constant marginal cost of 11. There are no fixed costs. Firm A chooses its quantity first and Firm B will then choose its own quantity to maximize it profit. i. Solve for Firm B's BR function as a function of qA: ii. Solve for Firm A's optimal output level given Firm B's Best Response Function. Solve for Firm B's profit maximizing output. iv. ii Solve for the market price that would prevail and each firm's profit. ow assume instead of acting sequentially, both firm A and B act simultaneously. v.Find the Cournot quantity per firm. vi. In which market situation are consumers better off and there is a lower dead weight loss, the Cournot or Stackelberg? Which would Firms A and B prefer?Explanation / Answer
i)
P = 100 – Q
TR(B) = 100Q – QB ^2 – QA QB
MR = 100 – 2QB – QA
MC = 10
Equilibrium:
100 – 2QB – QA = 10
90 = 2QB + QA
QB =( 90 –QA) / 2
ii)
since MC is constant here,
Hence it can be done directly
QA = (a-c) / 2B
= (100– 10) /2
= 90 /2
= 45
iii)
B profit maximization:
QB = (a-c) /4B
= 90 /4
= 22.5
iv)
Price = 100 – 67.5
= $ 32.5
Profit of A = 45 *32.5 – 45*10
= 1012.5
Profit of B = 22.5*32.5 – 22.5*10
= 506.25
v)
100 – Q = 10
Q = 90
Cournot output = (2/3)*90
= 60
Each firm will produce 30 units.
Since output is higher and price is power in Stackelberg Market, hence dead weight loss is also lower. Consumer will prefer Stackelberg Market.
Leader will prefers stackelberg Market situation since its profit would be higher here. while follower would go for Cournot.
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