This topic contains a solution. Click here to go to the answer

Author Question: Consider two Cournot competitors selling complementary goods with demand curves given by: p1 = ... (Read 38 times)

silviawilliams41

  • Hero Member
  • *****
  • Posts: 560
Consider two Cournot competitors selling complementary goods with demand curves given by:
 
  p1 = 100 - q1 + .5q2
   p2 = 100 - q2 + .5q1
  Suppose each firm has a marginal and average cost of 10.
  a. What about the demand equations indicate that these goods are complements? How do they differ from the standard Cournot model?
  b. Find the equilibrium prices and quantities.
  c. Suppose the two firms merge. By doing so, the newly merged firm will act to maximize the joint profits ((q1,q2 ) = 1(q1,q2 ) + 2(q1,q2 )). Find the joint-profit maximizing price and quantities.
  d. Are the combined profits greater or smaller from merging? That is, is merging profitable for the firms?
  e. Are consumers better or worse off with the firms merging? How does this compare to the mergers of Cournot competitors selling substitutes? What does this imply about antitrust policy towards mergers of firms selling complementary goods (such as airplanes and engines, computers and processors, cars and tire companies, etc).

Question 2

The above figure shows supply and demand curves for milk. If the government passes a law that establishes 3 per month as the legal minimum per gallon price, change in producer surplus will be
 
  A) b + c + d.
  B) b - f - g.
  C) c + d + g.
  D) b - g.



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question
Marked as best answer by a Subject Expert

frogdreck123456

  • Sr. Member
  • ****
  • Posts: 329
Answer to Question 1

a. The output of the rival firm actually increases the own firm's demand curve. Thus, these goods are complements rather than substitutes as in the typical model
b. The objective function of a firm is
= (100 - q1 + .5q2 )q1 - 10q1
The derivative is
100 - 2q1 + .5q2 - 10 = 0
q1 = (90 + .5q2 )/2
The firm's will produce where outputs are the same (symmetrical)
2q = 90 + .5q q = 60. Both firms produce 60 units. The price of each good is 70
c. The combined profit is:
= (100 - q1 + .5q2 )q1 - 10q1 + (100 - q2 + .5q1 )q2 - 10q2
The derivative w.r.t. q1 is
100 - 2q1 + .5q2 - 10 + .5q2 = 0
The outputs will be the same because the derivatives are symmetrical.
90 - q1 = 0
q1 = 90
So 90 units is produced by each firm (plant) for a total of 180 units. The price in each market is 55.
d. Greater
e. Consumers are better off because the price is lower and the quantity is higher in each market.

Answer to Question 2

D





 

Did you know?

A good example of polar molecules can be understood when trying to make a cake. If water and oil are required, they will not mix together. If you put them into a measuring cup, the oil will rise to the top while the water remains on the bottom.

Did you know?

When Gabriel Fahrenheit invented the first mercury thermometer, he called "zero degrees" the lowest temperature he was able to attain with a mixture of ice and salt. For the upper point of his scale, he used 96°, which he measured as normal human body temperature (we know it to be 98.6° today because of more accurate thermometers).

Did you know?

Aspirin may benefit 11 different cancers, including those of the colon, pancreas, lungs, prostate, breasts, and leukemia.

Did you know?

More than nineteen million Americans carry the factor V gene that causes blood clots, pulmonary embolism, and heart disease.

Did you know?

On average, someone in the United States has a stroke about every 40 seconds. This is about 795,000 people per year.

For a complete list of videos, visit our video library