Question

Wayne and Daryl are two individuals who one day simultaneously discover a stream that flows with apple flirtini instead of water. Wayne and Daryl each individually decide to bottle the apple flirtini and sell it. The marginal and fixed costs of bottling apple flirtini are both zero. The market demand for bottled apple flirtini is given as: P = 90 − 0.25Q where Q is the total quantity of bottled apple flirtini produced and P is the market price of bottled apple flirtini. (a) What price and quantity of bottled apple flirtini maximizes total economic surplus? (b) If Wayne and Daryl were to collude with one another and produce the profitmaximizing monopoly quantity of bottled apple flirtini, how much bottled apple flirtini will they produce? (c) Given the output level in (c), what price will Wayne and Daryl charge for bottled apple flirtini? (d) Suppose that instead Wayne and Daryl act as Cournot duopolists, what are the reaction functions for Wayne and for Daryl? (e) In the long run, what level of output will Wayne produce if Wayne and Daryl act as Cournot duopolists? (f) In the long run, what will be the price of bottled apple flirtini be if Wayne and Daryl act as Cournot duopolists?

Answer 1

a)

For maximum surplus,

P = MC =AC

MC = AC =0

So, they will produce until P becomes 0

Q = 90*4 = 360.

The economic surplus maximizing Q = 360 and P = 0  

b)

For profit maximization,

That is, for maximizing profits, they will produce 180 units.

c)

That is, they will charge 45 per bottle.

d)

For Wayne,

For profit maximization for Wayne,

This is the reaction function for Wayne.

Similarly, the reaction function for Daryl is,

e)

To find the long term output, we need to solve the reactions functions simultaneously.

That is, in the long run, both Wayne and Daryl produces 120 units each.

f)

That is, they charge a price of 30