Answer to Question #264798 in Microeconomics for manuewrz

Question

a.) Assume the demand for wine in a small isolated town is P = 200 - Q. Two fims, A and B are the sole producers of the product, and they display Cournot duopolists tendencies. Both firms have a same total cost function of TCi = 40 + Qi. Find the profit maximizing output level for each firm, market price and profit for each of the firm. [10marks] b.) The Chief Executive Officer of the town intents to subsidize firm A to raise its output to that of a Stackelberg leader, how large should the subsidy be in terms of output? [7 marks] c.) What happens in a duopoly if both firms try to act as the Stackelberg leader? [4 marks] d.) Briefly explain why the intersection of the best-response functions is the Cournot equilibrium [4 marks]

Answer 1

(a)

(1)

$P=200-Q$

$TR=PQ=(200-Q)Q$

$=200Q-Q^2$

$\pi=TR-TC$

$=(200Q-Q^2)-(40+Q)$

$=-40+199Q-Q^2$

$\frac{d\pi }{dQ}=199-2Q=0$

$\implies Q=99.5$

(2)

$P=200-Q$

$=200-99.5=100.5$

(3)

Profit for each firm:

$=-40+199(Q)-Q^2$

$=-40+199(99.5)-(99.5)^2$

$=9,860.25$

(b)

The subsidy should be large enough to cover the production cost of more than half of the output that is produced by firm A.

(c)

If both firms are sophisticated, then both of them will want to act as leaders. This is because, the action of being Stackelberg leaders yields greater profit to both of them at that position.

(d)

The intersection of the best response functions is the Cournot equilibrium because Cournot model assumes that, rival firms produce a homogeneous product, and each firm attempts to maximize profit by choosing how much to produce. All the firms usually choose the output simultaneously and the equilibrium that results is a Nash equilibrium in quantities.