Maximize total revenue, Financial Econometrics

The demand equation for Good Y is given by

            P = 900/q - 0.48q + 100       q > 0

In this question use derivatives to explore the relationship between the demand for Good Y, total revenue and elasticity.

Task

  1. Find an expression for the total revenue, TR.
  2. Find an expression for marginal revenue, MR.
  3. Find and interpret the marginal revenue when q = 60
  4. What price must be charged to achieve a demand of q = 60
  5. Find an expression for dp/dq and evaluate at q = 60
  6. Use the relationship  dp/dq = 1/dp/dq and the result of (4) and (5) to determine

     Whether the demand is elastic, unit elastic or inelastic when q = 60, and interpret  the result.

       7. Determine value of q which maximizes total revenue.

       8. What price must be charged to maximize total revenue?

      9. Complete the following table, giving the corresponding rang or value for price and quantity, and whether marginal revenue is positive, negative or zero for corresponding range or value.

Demand

 

Inelastic

 

Unit Elastic

 

Elastic

 

Price

 

 

 

Quantity

 

 

 

Marginal Revenue

 

 

 

Hints:

  • Do Not attempt to obtain an equation for dq/dp in terms of p.
  • A second derivative is required in question 7 to verify a maximum.
  • Graph TR to check/verify your algebraic answers.
Posted Date: 2/19/2013 1:22:24 AM | Location : United States







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