Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
bartleby

Concept explainers

Question
Book Icon
Chapter 15, Problem 15.1P

a)

To determine

Profit maximizing price quantity combination and corresponding profits for the monopolist

a)

Expert Solution
Check Mark

Explanation of Solution

Demand curve, Q=150P and costs is 0 .

Therefore, profits are,

π=PQ

=(150P)P

=150PP2

Differentiating the profit equation with respect to P to find the optimal value of P that maximises the profit for the monopolist. First order condition,

π=0

π=1502P=0

P=75

Q=15075=75

Second order condition, proves that this price and quantity maximizes the profits for a monopolist.

And profits given this price and quantity is,

π=PQ

=5625

b)

To determine

Nash equilibrium output for two firms operating in Cournot model. Also to compute

market output, price and firms profits.

b)

Expert Solution
Check Mark

Explanation of Solution

From the demand function, we get, P=150Q

Also, Q=q1+q2

So, profit for the firm 1 ,

π1=(150q1q2)q1

Differentiating with respect to q1 , to get the value of q1 that maximises the profits for firm 1. First order condition,

π1=1502q1q2=0

=2q1+q2=150

And similarly, profit equation of the firm 2 reveals,

=2q1+q2=150 (2)

Solving 1 and 2 we get, q1+q2=50

Market output will be, Q=100

And market price is,

P=150100=50

So, at P=50 and q1=q2=50

The profits for firm 1 is,

π1=50×50=2500

The profit for firm 2 is,

π2=50×50=2500

c)

To determine

To find Nash equilibrium prices in a Bertrand model. Also to compute firm output and profits as well as market output.

c)

Expert Solution
Check Mark

Explanation of Solution

In case of a Bertrand model, undercutting of prices by both the firms leads to price becoming approximately nil in the given scenario. Hence the price will tend to zero, and quantity will become tending to 150 .

So, price =0

And Quantity =150

As there are no cost to production so firms will undercut to a level that at the end of the day both firms will be willing to provide the quantity at price 0 .

Profits for the firm =0

And market output is,

=150+150=300

However the maximum demand is only for 150 units, therefore market output is 150 .

d)

To determine

To graph the demand curve for cases in parts (a), (b), (c).

d)

Expert Solution
Check Mark

Explanation of Solution

Microeconomic Theory, Chapter 15, Problem 15.1P

In the above diagram, Price is measured on y -axis and quantity is measured on x -axis. In part a , where the firm is a monopolist produces 75 units of quantity and sells it at $75 per unit.

In part b , there are two firms, so price gets reduced to $50 per unit and quantity produced is 100 units.

In part c, the two firms follows Bertand equilibrium model, quantity produced is 150 units with 0 price per unit.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Consider a "Betrand price competition model" between two profit maximizing widget producers say A and B. The marginal cost of producing a widget is 4 for each producer. Each widget producer has a capacity constraint to produce only 5 widgets. There are 8 identical individuals who demand 1 widget only, and individuals value each widget at 6. If the firms are maximizing profits, then which of the following statement is true: a) Firm A and Firm B will charge 4 b) Firm A and Firm B will charge 6 c) Firm A and Firm B will charge greater than or equal to 5 d) None of the options are correct.  Explain clearly.
Consider two price-setting oligopolies supplying consumers in a certain region of a country. Firm 1 employs many of the people living there and the local government subsidizes its operations. In all other respects, the firms are identical-they have the same constant marginal cost, MC = 4, and produce the same good. The demand function for Firm 1 is q1 = 600 - 50p1 - 20p2 and for Firm 2 is q2 = 600 - 50p2 - 20p1, where p1 is Firm 1's price and p2 is Firm 2's price. a. What are the Nash-Bertrand equilibrium prices and quantities without the subsidy? b. What are they if Firm 1 receives a per-unit subsidy of S = 1? Compare the two equilibria.
Firm 1 and firm 2 are Bertrand duopoloists. Firm 1 has a marginal cost of $6.00 per unit, and firm 2 has a marginal cost of $8.01 per unit. The demand for their product is p=23.00−Q, where Q is the total quantity demanded. How much does each firm sell in equilibrium? Assume that prices can only be set to the nearest cent, firms split the market if they set the same price, and there are no fixed costs. Firm 1 production:______ Firm 2 production:______ What are the profits for each firm in equilibrium? Firm 1 profit: $______ Firm 2 profit: $______
Knowledge Booster
Background pattern image
Economics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Microeconomic Theory
Economics
ISBN:9781337517942
Author:NICHOLSON
Publisher:Cengage
Text book image
Managerial Economics: Applications, Strategies an...
Economics
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:Cengage Learning
Text book image
Micro Economics For Today
Economics
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Cengage,
Text book image
Economics For Today
Economics
ISBN:9781337613040
Author:Tucker
Publisher:Cengage Learning
Text book image
Survey Of Economics
Economics
ISBN:9781337111522
Author:Tucker, Irvin B.
Publisher:Cengage,