exercise 4 13
Download
Skip this Video
Download Presentation
Exercise 4.13

Loading in 2 Seconds...

play fullscreen
1 / 13

Exercise 4.13 - PowerPoint PPT Presentation


  • 110 Views
  • Uploaded on

Exercise 4.13. MICROECONOMICS Principles and Analysis Frank Cowell. November 2006 . Ex 4.13(1) Question. purpose : to derive a simple model of monopoly regulation with a welfare evaluation using CV method : build model up step-by-step through the question parts. Ex 4.13(1) .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Exercise 4.13' - nairi


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
exercise 4 13

Exercise 4.13

MICROECONOMICS

Principles and Analysis

Frank Cowell

November 2006

ex 4 13 1 question
Ex 4.13(1) Question
  • purpose: to derive a simple model of monopoly regulation with a welfare evaluation using CV
  • method: build model up step-by-step through the question parts
ex 4 13 1
Ex 4.13(1)
  • A natural monopoly requires that costs be subadditive
  • Subadditivity implies the following
    • given an integer m > 1
    • C(w, q) < mC(w, q/m)
    • (see Ex 3.1)
  • In the present case costs are C0 + cq
  • Clearly m[C0 + cq/m] = mC0 + cq > C0 + cq
ex 4 13 2 question
Ex 4.13(2) Question

Method:

  • Find monopolist’s AR from consumer demand using answer to Ex 4.12.
  • Then use standard optimisation procedure
ex 4 13 2 monopoly profits
Ex 4.13(2) Monopoly profits

Aggregate demand over N consumers using Exercise 4.12

Rearrange to get AR curve:

Total Revenue is:

Profits are therefore:

ex 4 13 2 maximising profits
Ex 4.13(2) Maximising profits

FOC (MC = MR) yields:

So monopolist’s optimal output is:

From AR curve, price at optimum is:

Simplify this to:

(clearly price > MC)

ex 4 13 3 question
Ex 4.13(3) Question

Method:

Aggregate the CV for each consumer to define L.

Use marginal cost and monopolist’s equilibrium price to evaluate L

ex 4 13 3 evaluating loss
Ex 4.13(3) Evaluating loss

Use definition of CV with p1' = c:

Evaluate L at p1 = 2c:

Firm’s profits are:

Clearly L > profits

ex 4 13 4 question
Ex 4.13(4) Question

Method:

Add bonus B into the expression for profits

Again use standard optimisation procedure

ex 4 13 4 evaluating profits again
Ex 4.13(4) Evaluating profits (again)

Profits including bonus are:

Value of bonus is:

Use demand curve to express this in terms of q:

So profits can now be expressed as:

ex 4 13 4 evaluating profits again1
Ex 4.13(4) Evaluating profits (again)

Take the expression for profits including bonus

FOC for a maximum is again MR = MC:

Rearranging we get the value of optimal output for the regulated monopolist:

Use demand curve to find:

Clearly the regulated price = MC:

ex 4 13 points to note
Ex 4.13: Points to note
  • Aggregate welfare loss is found from individual CV
  • Unregulated monopoly makes profits smaller than losses to consumer
  • Regulation causes monopoly to behave like competitive firm
ad