Question 4: Oligopoly (15 point) Assume the demand for a product is given by P=1

Question

Question 4: Oligopoly (15 point) Assume the demand for a product is given by P=150-Q (a) Assume there are 2 firms and MC- AVT 30 and FC 0. If both firms try to underbid each other in price, how low can price can go? Explain (b) What will be the price, quantity produced and Economic profit of each firm in (a)? (c) Now assume you have the same cost structure than in (a) but the firms form a Cartel to monopolize the market. Obtain the price, quantity produced and economic profit of the monopoly assuming of course that both firms are going

Explanation / Answer

Consider the given problem, here we have given the inverse demand curve of the market which is given by, “P=150-Q”, here “Q”, be the total production produced by 2 firms.

So, both of them have same MC=30. Here each firm want to underbid its “P” compared to the rival firm, so that the firm will be able to capture the entire market. So, both of them reduce their price, here goods is totally identical, so buyer will purchase the good from the firm, which will supply at a lower price.

So, both of them reduce the “P”, and finally this “price” competition will end up at,P1=P2=MC=30, because they can’t reduce their price further. If they do so they have to incur loses.

So, the minimum “P”, be “P=30”.

b).

So, here P=30, => Q=150-P=150-30=120. So, the total production is, “Q=120 and P=30. Now, there are 2 producers and they will charge same price, => they will capture equal share of the market, => they will produce same amount, => q1=q2=120/2=60.

Since here P=MC=30,=> here the economic profit earn by 2 firms is “0”.

c).

now, suppose both firms form a cartel to monopolize the market. So, the market demand be,

“P=150-Q, => MR=150-2*Q. Now, the optimum quantity under monopoly market is given by, “MR=MC”.

=> MR=150 – 2*Q = 30, => 2*Q = 150 – 30 = 120, => Q=120/2=60, => here optimum quantity is Q=60.

So, at Q=60, P=150-Q=150-60=90. So the monopoly “price” and “quantity” combination is given by, “P=90” and “Q=60”.

So, the profit be, “Profit = P*Q – MC*Q = (90 – 30)*60 = 60*60 = 3600 > 0. So, they will equally share the total profit, => each firm will get, 3600/2=1800 > 0.

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