Supply and Demand and Firm

CHAPTER 9

OLIGOPOLY AND FIRM ARCHITECTURE

1. The demand function for a product sold by an oligopolist is given below:
QD = 370 – P
The firm’s marginal cost function is given below:
MC = 10 + 4Q
Calculate the equilibrium price and quantity.

Solution:
P = 370 – Q so TR = 370Q – Q2 and MR = 370 – 2Q
MR = 370 – 2Q = 10 + 4Q = MC so Q = 60 and P = 310

2. The demand function for a product sold by an oligopolist is given below:
QD = 135 – 0.5P
The firm’s marginal cost function is given below:
MC = 30 + 4Q
Calculate the equilibrium price and quantity.

Solution:
P = 270 – 2Q so TR = 270Q – 2Q2 and MR = 270 – 4Q
MR = 270 – 4Q = 30 + 4Q = MC so Q = 30 and P = 210

3. An oligopolist is currently charging a price of …show more content…

A market that follows the price leadership of a barometric firm has the following demand function:
QDM = 1400 – 2P
The follower firms have the following aggregate marginal cost function:
MCF = 100 + 0.50QMC
The barometric firm has a horizontal marginal cost curve equal to $300. Determine total industry output, market price, and the division of output between the barometric firm and the follower firms.

Solution:
The barometric firm 's demand function (QDL) is determined by taking the horizontal difference between the market demand function and the followers ' aggregate marginal cost function when P = MCF as follows:
QMC = 2MCF – 200 so QDL = QDM – QMC = 1400 – 2P – 2P + 200 = 1600 – 4P
The barometric firm 's marginal revenue function is:
P = 400 – 0.25QDL so MR = 400 – 0.5QDL
The barometric firm will produce the quantity of output that equates its marginal cost with the marginal revenue associated with its demand function:
MC = 300 = 400 – 0.5QDL = MR so QDL = 200 and P = 350
The follower firms take the price determined by