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 $600 and is selling 300 units of output per day. If the firm increases price above $600, then quantity demanded will decline by 3 units for every $1 increase in price. If the firm reduces price below $600, then the quantity demanded will increase by 1.5 units for every $1 decrease in price. If the firm 's marginal cost curve is horizontal, within what range could marginal cost vary without giving the firm an incentive to change price or quantity?
Solution:
The kinked demand curve model applies here. At prices above $600, the demand and marginal revenue functions are:
Q = 2100 – 3P so P = 700 – (1/3)Q and MR = 700 – (2/3)Q
At prices below $300, the demand and marginal revenue functions are:
Q = 1200 – 1.5P so P = 800 – (2/3)Q and MR = 800 – (4/3)Q
The firm will continue to charge a price of $600 so long as the optimal level of output is 300 units. Q = 300 will be optimal so long as MC is between the two values of MR located at the kink. Thus, MR = 700 – (2/3)(300) = 500 is the upper limit of MC and MC = 800 – (4/3)(300) = 400 is the lower limit of MC.
4. An oligopolist is currently charging a price of $100 and is selling 400 units of output per day. If the firm increases price above $100, then quantity demanded will decline
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 $600 and is selling 300 units of output per day. If the firm increases price above $600, then quantity demanded will decline by 3 units for every $1 increase in price. If the firm reduces price below $600, then the quantity demanded will increase by 1.5 units for every $1 decrease in price. If the firm 's marginal cost curve is horizontal, within what range could marginal cost vary without giving the firm an incentive to change price or quantity?
Solution:
The kinked demand curve model applies here. At prices above $600, the demand and marginal revenue functions are:
Q = 2100 – 3P so P = 700 – (1/3)Q and MR = 700 – (2/3)Q
At prices below $300, the demand and marginal revenue functions are:
Q = 1200 – 1.5P so P = 800 – (2/3)Q and MR = 800 – (4/3)Q
The firm will continue to charge a price of $600 so long as the optimal level of output is 300 units. Q = 300 will be optimal so long as MC is between the two values of MR located at the kink. Thus, MR = 700 – (2/3)(300) = 500 is the upper limit of MC and MC = 800 – (4/3)(300) = 400 is the lower limit of MC.
4. An oligopolist is currently charging a price of $100 and is selling 400 units of output per day. If the firm increases price above $100, then quantity demanded will decline