Ecos3005

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Ecos3005

Question 1

A market with demand Q = 16p 2 is supplied by a monopoly with costs C(Q) = 6 + Q2 . Calculate the equilibrium price, output and monopoly profits. What would be the equilibrium if the market were supplied competitively by firms, and each firm had the same cost function as the monpolist

Question 2

An industry consists of two firms with identical costs C(q) = 5q + q2 . The firms can either “collude”or “compete”. The market demand is Q = 125 p.

1. If both collude, they each produce half of the monopoly output, qm = Qm /2. Calculate the output and profits for each firm in this situation.

2. If both compete, they play Cournot and each produce qc . Calculate the output and profits for each firm in this situation.

3. If one firm colludes and the other competes, the latter produces the output that maximizes its profits given that the other other firm produces qm . Call this output q . Calculate the output and profits for each firm in this situation.

4. Represent your results in a normal-form game. What is the Nash Equilibrium if the game is played only once

Question 3

What are the key assumptions in the Dominant-Firm model

Question 4

A perfectly competitive market is supplied by 50 low cost firms, each with a cost curve C (q) = 350 + 2q + q2 . There are also n high-cost firms, each with cost curve Ch (q) = 400 + 2q + q2 . Market demand is Q = 2500 10p.

1. If none of the high cost firms makes a positive profit, how large is n

2. How much profit do the low-cost firms make

Hint: note that the firms only differ in their fixed costs.