Purchase Solution

Analyising Monopolist's demand and cost functions

Not what you're looking for?

Ask Custom Question

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

Purchase this Solution
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:
Lokesh Jain, MSc
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!"
Purchase this Solution
Free BrainMass Quizzes
Elementary Microeconomics

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

Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Economics, Basic Concepts, Demand-Supply-Equilibrium

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

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.

View More Free Quizzes
Related BrainMass Solutions

  • 5 Problems

    (a) Using calculus, derive the relationship between a monopolist's marginal revenue, the monopolists' price, and the price elasticity of demand. (b) Consider a monopolist who produces output at a constant marginal and average cost of $12.

  • Monopolist profit maximization after tax and with price ceiling

    the monopolist's quantity and profits in case the government fixes a p = 90. a) Profit is maximized at the quantity where Marginal Revenue (MR) = Marginal Cost (MC) From the Demand curve: Q = 186 - P Rearranging: P = 186 - Q Total Revenue (TR

  • Calculating marginal and average products, and Lerner Index

    Suppose the demand curve for a monopolist is QD= 500 - P, and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit. a.

  • Maximizing Total Profits and Revenue

    82909 Maximizing Total Profits and Revenue A Monopolist's Demand and Total Cost functions are: P= 1624 -4Q TC= 22,000 + 24Q -4Q(squared) + 1/3Q (to the third power) Where Q is output produced and sold a.

  • Calculating the profit maximizing price and quantity

    = 140.31 TC = 10 + 5Q + Q^2 TC = 96.73 Profit = TR - TC Profit = 140.31 - 96.73 Profit = 43.57 Detailed calculations of a monopolist's profit maximizing price and output given its Demand and Total Cost functions.

  • monopolistis quantity, price and profit

    Calculate the monopolist's profit-maximizing quantity, price and profit Demand = 1000 - 10P Let the price be 'P', therefore total revenue = demand x price = 1000P - 10P^2 Total Cost = $10Q; but from above, Q = 1000 - 10P, so total cost = 10,000

  • Calculate the optimal parameters in the given case.

    Markup formula gives us Optimal Price = (Ep/(1+Ep))* MC Where Ep is price elasticity of demand and MC is marginal cost.

  • Finding optimal number of output

    Suppose that Figure 7.4 shows a monopolist's demand curve, marginal revenue, and its costs. At the profit maximizing output level, what would be the monopolist's profit?

  • Lerner Index: Finding Monopolist's Profit Maximizing Output

    228260 Lerner Index: Finding Monopolist's Profit Maximizing Output Suppose the demand curve for a monopolist is QD = 500 - P, and the marginal revenue function is MR = 500- 2Q.

  • monopolist's marginal cost

    70966 Monopolist's marginal cost A monopolist is profit maximizing where the elasticity of demand is -2 and price is $4. What is the monopolist's marginal cost?

View More Related Solutions