Answer to Question #89691 in Microeconomics for Talha

Question

The demand for spring water is P=1000-QT and marginal cost is zero . There are two firms in the market and each firm believes that the other will respond to one unit decrease in output by increasing its output by one half unit. For example if firm 1 reduces output by one unit, firm 2 will respond by increasing its output by one half unit.
a. Compute marginal revenue equation for each firm
b. Compute reaction functions for each firm
c. What will be equilibrium price and quantity and total output for industry?

Answer 1

a. Marginal revenue equations are:

MR1 = TR(Q1)' =((1000 - Q1 - Q2)×Q1)' = 1000 - 2Q1 - Q2.

MR2 = 1000 - 2Q2 - Q1.

b. Reaction functions for each firm are:

MR = MC,

1000 - 2Q1 - Q2 = 0,

Q1 = 500 - 0.5Q2,

Q2 = 500 - 0.5Q1.

c. What will be equilibrium price and quantity and total output for industry are:

Q1 = 500 - 0.5×(500 - 0.5Q1),

0.75Q1 = 250,

Q1 = 333.33 units = Q2.

QT = Q1 + Q2 = 667 units.

P = 1000 - 667 = 333.