Purchase Solution

# Analyising Monopolist's demand and cost functions

Not what you're looking for?

Suppose the demand curve faced by a monopolist is:

q=p^-a where a>0

The total cost for the monopolist are C=sq

a) Find the profit maximizing level of output.
b) Specify the first and second order condition for profit maximization.
c) What is the price elasticity of demand faced by this monopolist
d) What happens to the profit maximizing level of output as s increases
e) What happens to the profit maximizing level of output as a increases.
f)Explain results

##### Solution Summary

Solution describes the steps for determining profit maximizing output and elasticity of demand. It also discusses first and second order conditions for profit maximization.

##### Solution Preview

Please refer the attached file for complete description. Work done with the help of equation writer may not print here.

a) Find the profit maximizing level of output.

A monopolist will produce output to maximize profits in such a way that MC=MR

Total cost =C=sq

Marginal cost = MC=dC/dq=s

Total Revenue = price*output

Given q=p^-a

Total revenue = p*q=

For profit maximization MR=MC

b)Specify the first and second order condition for profit maximization.

Profit =Total revenue-Total cost

First order condition:
Put
d(Profit)/dq=0

d(Profit)/dq=d(TR)/dq-dC/dq=0

we know that d(TR)/dq=MR

and dC/dq=MC

d(Profit)/dq=d(TR)/dq-dC/dq=0
=MR-MC=0
i.e. MR=MC

We lead to same condition as we have used in part (a), so we can directly use the results here and can say that first order ...

Solution provided by:
###### Education
• BEng (Hons) , Birla Institute of Technology and Science, India
• MSc (Hons) , Birla Institute of Technology and Science, India
###### Recent Feedback
• "Thank you"
• "Really great step by step solution"
• "I had tried another service before Brain Mass and they pale in comparison. This was perfect."
• "Thanks Again! This is totally a great service!"
• "Thank you so much for your help!"

##### Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

##### Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

##### Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

##### Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

##### Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.