616 words - 3 pages

Consider the following industry conditions in answering the following problems:

Market Demand: Q = 120 – P

Constant Marginal Cost: MC = AC = 24 (No Fixed Costs)

1. Find the industry price and output if the above industry was perfectly competitive. Find the industry price, output, and profits if the above industry was a monopoly. (10 points)

Perfect Monopoly

P=24 P=120-Q P=120-48

Q=120-24 MR=120-2Q P=72

Q=96 24=120-2Q

2Q=96 π=48(72-24)

Q=48 π=2304

2. Assume that two Cournot duopolists confront the above industry conditions.

a. Find each firm’s reaction function and graphically draw the reaction curves for both firms. (10 points)

P=120-q1-q2

TR1=P*q1 TR2=P*q2

TR1=(120-q1-q2)*q1 TR2=(120-q1-q2)*q2

TR1=120q1-q1^2-q1q2 TR2=120q2-q1q2-q2^2

MR1=120-2q1-q2 ...view middle of the document...

Cournot tends to lie somewhere in the middle of these to markets.

3. Now consider the Stackelberg model which is a two stage sequential game. In this model, assume that Firm 1 can commit to an output choice (in stage 1) before Firm 2 can choose its output (in stage 2). Assume that the two firms face the same industry conditions as shown above.

a. Find firm 1’s residual demand curve. [Hint: Use firm 2’s reaction function that you found in 2a] (10 points)

q2=48-1/2q1

P=120-q1-(48-1/2q1)

P=120-q1-48+1/2q1

P=72-1/2q1

b. Find the quantities for both Firm 1 and Firm 2 that defines a Stackelberg equilibrium. (10 points)

MR=72-q1 q2=48-1/2q1

24=72-q1 q2=48-1/2(48)

q1=48 q2=24

c. What is the level of profits that each firm will make? Show all your work. (10 points)

P=120-48-24

P=48

π 1=48(48-24) π2=24(48-24)

π 1=1152 π2=576

4. Consider two identical Bertrand duopolists that confront the above industry conditions.

a. Find the industry price, output, and profits for this situation. (10 points)

P=MC

P=24

24=120-Q

Q=96

π =96(48-24)

π=2304

b. Explain why the Bertrand equilibrium differs from the Cournot equilibrium? Under what conditions will the Cournot equilibrium be more realistic? Under what conditions will the Bertrand equilibrium be more realistic? (10 points)

Bertrand differs, because the firms are trying to undercut each other, where as Cournot firms pick a specific quantity. Cournot equilibrium is competition on quantity and is usually nicer to deal with. Also Cournot tends to lead to bigger profits. Bertrand equilibrium is more realistic when there is competition on price, with little for profit. It is also more vigorous to deal with.

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