3. Two firms, firm 1 and 2, compete by choosing quantity. The inverse market dem

Question

3. Two firms, firm 1 and 2, compete by choosing quantity. The inverse market demand function is P- 250-0 Each firm's marginal cost is 10. Suppose that firm 1 sets its quantity first and then firm 2 sets its quantity after observing firm 1's decision. What quantity will each firm produce? 4. Suppose that the marginal benefit of a public good for consumer 1 is given by MB -10-2q.and MB -20-4qfor consumer 2. The marginal cost to produce the public good is 6. What level is the efficient level of production for the public good? 5. Find all the Nash equilibrium or equilibria in the following payoff matrix.-(L)3L Player 2 Left 7, 3 2,-1 Right 1, 2 5,1 Top Player 1 Bottom

Explanation / Answer

Question 3

In Stackelberg model where firm 1 is a first mover, it must take the reaction function of firm 2 in its computation of marginal revenue. let the demand function be P = 250 – q1 – q2. MC is $10 for both firms

Derivation of firm 2’s reaction function

Total revenue of firm 2 = P*(q2) = (250 – (q1 + q2))q2 = 250q2 – q22 – q1q2

Marginal revenue = 250 – 2q2 – q1

Marginal cost = 10

Solve for the reaction function

250 – 2q2 – q1 = 10

2q2 = 240 – q1

q2 = (120 – 0.5q1)

Incorporate this in the reaction function of firm 1

Total revenue for firm 1 = P*(q1) = (250 – (q1 + q2))q1

= (250 – q1 – (120 – 0.5q1))q1

= (250 – q1 – 120 + 0.5q1)q1

= (130 – 0.5q1)q1

MR = 130 – q1

Equate MR = MC

130 – q1 = 10

q1 = 120

q2 = (120 – 0.5q1) or 120 – 60 = 60 units.

Firm 1 produces 120 units and firm 2 produces 60 units.

Question 4

For public good and its efficient quantity, find the social marginal benefit curve which is the sum of all MB curves

SMB = MB1 + MB2 = 10 - 2q + 20 - 4q = 30 - 6q

MC = 6. Hence the efficient quantity of public good is found when MR = MC

30 - 6q = 6

q* = 4 units.

Question 5

There are two Nash equilibria, Top, Left and Bottom, right. This is because no player has dominant strategy. Player 1 selects Top when player 2 selects Left and Bottom when he selects Right. Similarly, Player 2 selects Left when player 1 selects Top and selects Right when he selects bottom. Hence these two choices are made simultaneously.

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