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Exercise 4.13

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) .

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Exercise 4.13

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  1. Exercise 4.13 MICROECONOMICS Principles and Analysis Frank Cowell November 2006

  2. 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

  3. 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

  4. Ex 4.13(1): “Natural monopoly” AC c q

  5. Ex 4.13(2) Question Method: • Find monopolist’s AR from consumer demand using answer to Ex 4.12. • Then use standard optimisation procedure

  6. 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:

  7. 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)

  8. 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

  9. 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

  10. Ex 4.13(4) Question Method: Add bonus B into the expression for profits Again use standard optimisation procedure

  11. 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:

  12. 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:

  13. 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

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