Download Quiz 5

Student Number
ECON212 Quiz 5
1.
A monopolist faces a demand curve P  700  5Q , and initially faces a constant
marginal cost MC  100 .
a)
Calculate the profit-maximizing monopoly quantity and price and compute
the monopolist’s total revenue at the optimal price. (1.5 points)
Answer
With demand P  700  5Q , MR  700  10Q . The monopolist will
produce an output where MR  MC .
700  10Q  100
600  10Q
Q  60
We find price by plugging the optimal value of Q into the demand curve.
P  700  5Q
P  700  300
P  400
Total revenue equals price times quantity. TR  400(60)  24, 000 .
Page Reference: 473
b)
Suppose that the monopolist’s marginal cost increases to MC  200 .
Verify that the monopolist’s total revenue goes down. (1 point)
Answer
Following the process described in part a),
700  10Q  200
10Q  500
Q  50
P  700  5Q
P  700  250
P  450
TR  PQ
TR  450(50)
TR  22,500
Thus, total revenue falls when compared to part a).
Student Number
ECON212 Quiz 5
Page Reference: 473
c)
Suppose that all firms in a perfectly competitive equilibrium had marginal
cost MC  100 . Find the long-run perfectly competitive industry price
and quantity. (1.5 points)
Answer
If all firms in a competitive market had MC  100 , setting P  MC (the
optimality condition for a perfectly competitive firm) implies
700  5Q  100
600  5Q
Q  120
At this quantity, price will be P  100 . Total revenue will equal price
times quantity. TR  100(120)  12, 000 .
Page Reference: 497-499
d)
Suppose that all firms’ marginal costs increased to MC  200 . Verify that
the increase in marginal cost causes total industry revenue to go up. (1
point)
Answer
Following the approach described in part c),
700  5Q  200
500  5Q
Q  100
P  200
TR  200(100)  20, 000
Thus, total revenue increases from part c).
Page Reference: 497-499
2.
Consider a market in which market demand is given by P  300  Q and every
firm has a constant marginal cost of $30.
a)
If this market were perfectly competitive, what would the equilibrium
price and quantity be? (1.5 points)
Student Number
ECON212 Quiz 5
Answer
To find the equilibrium, set P  MC . In this case
300  Q  30
Q  270
At this quantity, the market equilibrium price will be $30.
Page Reference: 567-568
b)
Suppose there are only two firms in this market and that these firms are
Bertrand competitors. What will the market equilibrium price and
quantity be? Explain how you arrived at your answer. (1.5 points)
Answer
In a Bertrand oligopoly, the equilibrium will occur when both firms charge
a price equal to their marginal cost. If either firm tries to charge a higher
price, the other firm will undercut the price and capture all of the market.
Thus, in this market, the equilibrium price is $30 and the equilibrium
quantity is therefore 270 units – the same as the perfectly competitive
solution.
c)
Page Reference: 567-568
Suppose there are only two firms in this market and that these firms are
Cournot competitors. What will the market equilibrium price and quantity
be? (2 points)