December 20, 2014

Homework Help: Microeconomics - Cournot

Posted by Anonymous on Tuesday, November 24, 2009 at 8:28pm.

X is a monopolist of a soda source that costlessly burbles forth as much soda as X cares to bottle. It costs X $2 per gallon to bottle this soda. The inverse demand curve for X’s soda is p(y) = 20 – 0.2y, where p is the price per gallon and y is the number of gallons sold.

a) What is the profit function? Find the profit-maximizing choice of y for X.

Profit = Y(P – AC) = Y(20 – 0.2Y – 2) = Y(18 – 0.2Y) = 18Y – 0.2Y^2
MC = 2
MR = 20 – 0.4Y
2 = 20 – 0.4Y
0.4Y = 20 – 2
Y = 45

b) What price does X get per gallon of soda if he produces the profit-maximizing quantity? How much profit does he make?

P = 20 – 0.2(45) = 11
Profit = 18(45) – 0.2(45)^2 = 405

c) Suppose that X’s neighbour, Z, finds a soda source that produces soda that is just as good as X’s soda, but it costs Z $6 a bottle to get his soda out of the ground and bottle it. Total market demand for soda remains as before. Suppose that X and Z each believe that the other’s quantity decision is independent of his own. What is the Cournot equilibrium output for Z? What is the price in the Cournot equilibrium?

I don’t know how to solve for this question.

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