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.

- Microeconomics - Cournot -
**economyst**, Wednesday, November 25, 2009 at 9:27am
a) I agree

b) I agree

c) Cournot models can be tricky beasts. But in this example, I believe the soulution is easy because 1) both firms have flat MC curves and MCx < MCz. I believe firm X, in the end, will drive P down to 6 and Z will produced nothing. (I wish I had more time to work the math, but I dont).

Lotsa luck.

## Answer This Question

## Related Questions

- statistics - The volumes of soda in quart soda bottles are normally distributed...
- English - e.g. I have a soda to recommend. ( What is 'soda'? Are both Coke and ...
- Statistics - A machine is used to fill soda bottles in a factory. The bottles ...
- General - a beverage company receives an order from the local colleges cafeteria...
- health - 1.Why is soda considered bad for your teeth, particularly if you do not...
- health - What is soda or soda pop? Is coke soda? What other drinks is soda? ...
- Algebra - at a baseball concession stand 3 hot dogs and 2 cups of soda together...
- college math - The ratio of soda to diet soda in Bill's Supermarket is 8 to 9. ...
- Physics - A con of soda displaces 3.79 * 10^-4 m^3 of water when completely ...
- math - Anthony went to the store to buy soda. There was a sign that said, "15% ...

More Related Questions