Finding the optimal output level
Not what you're looking for?
Suppose a firm in an oligopolistic industry faces the following demand curve:
P = 4,800 - 0.4 Q for Q < 3,000
P = 20,000 - 2 Q for Q > 3,000
Suppose further its Cost function is as follows:
TC = 1,000 + 100Q + 0.5 Q2
a. What price do you suppose they will charge in the short run?
b. What do you suppose will happen in the long-run?
The McCauley Company hires a marketing consultant to estimate the demand function for its product. The consultant concludes that this demand function is Q = 100P2.91I -2.3A0.4
Where Q is the quantity demanded per capita per month, P is the product's price (in dollars), I is per capita disposable income (in dollars), and A is the firm's advertising expenditures (in thousands of dollars).
a. What is the price elasticity of demand?
b. Will price increases result in increases or decreases in the amount spent on McCauley's product?
c. If the t-statistic to Part A was -1.5, would you rely on this estimate?
d. What is the advertising elasticity of demand?
Purchase this Solution
Solution Summary
Solution depicts the steps to find the optimal output level in the given case.
Solution Preview
I. The McCauley Company hires a marketing consultant to estimate the demand function for its product. The consultant concludes that this demand function is Q = 100P2.91I -2.3A0.4
Where Q is the quantity demanded per capita per month, P is the product's price (in dollars), I is per capita disposable income (in dollars), and A is the firm's advertising expenditures (in thousands of dollars).
a. What is the price elasticity of demand?
Q=100P^2.91*I^(-2.3)*A^0.4
Differentiate with respect to P, we get
dQ/dP=2.91*100P^(2.91-1)*I^(-2.3)*A^0.4=2.91*100P^1.91*I^(-2.3)*A^0.4
Price elasticity of demand=(dQ/dP)*(P/Q)
= 2.91*100P^1.91*I^(-2.3)*A^0.4*P/[100P^(-2.91)*I^(-2.3)*A^0.4]
= 2.91*P^1.91*P/P^2.91
= 2.91
It's a surprising result. Price elasticity of demand should be negative.
There might be some error in typing demand function, it could be
Q=100P^(-2.91)*I^(-2.3)*A^0.4
Differentiate with respect to P, we get
dQ/dP=-2.91*100P^(-2.91-1)*I^(-2.3)*A^0.4=-2.91*100P^(-3.91)*I^(-2.3)*A^0.4
Price elasticity of demand=(dQ/dP)*(P/Q)
...
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
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.
Elementary Microeconomics
This quiz reviews the basic concept of supply and demand analysis.
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.