Duopoly quantity setting firms face the market demand P=150- Q. Each firm has a

Question

Duopoly quantity setting firms face the market demand P=150- Q. Each firm has a marginal cost of £60 per unit. What is the Stackelberg equilibrium when Firm 1 moves first? i). Q1 =30, Q2 =30, P=90. ii). Q1 =45, Q2 =22.5, P=82.5. iii). Q1 =35, Q2 =30, P=100. iv). Q1 =40.5, Q2 =25.5, P=70.

d. What is the advantage to mixed strategies? They i). allow a player to be unpredictable. ii). allow a player to raise his maximin payoff. iii). are needed to guarantee the existence of equilibrium. iv). all of the above.

e. Lotteries A and B have the same expected value, but B has larger variance. Which of the following is true? i). some risk averse decision makers will prefer lottery A while others will prefer lottery B. ii). all risk averse decision makers will prefer lottery B to lottery A. iii). some risk neutral decision makers will prefer lottery A while others will prefer lottery B. iv). none of the above.

f. Which of the following is the present value of £1 payable in three years is: i). £1 ii). £1/(1+3r) iii). £1/(1-3r) iv). £1/(1+r)3

Explanation / Answer

Duopoly:

P = 150 – Q

P = 150 – (Q1 + Q2)

TR = PQ1 = 150Q1 – Q1^2 – Q1Q2

MR = Derivative of TR with respect to Q1

       = 150 – 2Q1 – Q2

MC = 60

The equilibrium condition is MR = MC

150 – 2Q1 – Q2 = 60

2Q1 + Q2 = 90 ……………………………(1)

Again, TR = PQ2 = 150Q2 –Q1Q2 – Q2^2

MR = Derivative of TR with respect to Q2

       = 150 – Q1 – 2Q2

MC = 60

The equilibrium condition is MR = MC

150 – Q1 – 2Q2 = 60

Q1 + 2Q2 = 90……………………………..(2)

Solving equation 1 and 2, Q1 = 30, Q2 = 30

Putting the values of Q1 and Q2 in P = 150 – (Q1 + Q2)

P = 150 – (30 + 30) = 90

Answer: Q1 = 30, Q2 = 30, P = 90

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