Frank Cowell: Microeconomics Exercise 4.13 MICROECONOMICS Principles and Analysis Frank Cowell November 2006

Frank Cowell: Microeconomics Ex 4.13(1) Question purpose: to derive a simple model of monopoly regulation with a welfare evaluation using CV 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 method: build model up step-by-step through the question parts

Frank Cowell: Microeconomics Ex 4.13(1) A natural monopoly requires that costs be subadditive A natural monopoly requires that costs be subadditive Subadditivity implies the following 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 C 0 + cq In the present case costs are C 0 + cq Clearly m[C 0 + cq/m] = mC 0 + cq > C 0 + cq Clearly m[C 0 + cq/m] = mC 0 + cq > C 0 + cq

Frank Cowell: Microeconomics Ex 4.13(2) Question Method: Find monopolist’s AR from consumer demand using answer to Ex Find monopolist’s AR from consumer demand using answer to Ex Then use standard optimisation procedure Then use standard optimisation procedure

Frank Cowell: Microeconomics Ex 4.13(2) Monopoly profits Aggregate demand over N consumers using Exercise 4.12 Aggregate demand over N consumers using Exercise 4.12 Rearrange to get AR curve: Rearrange to get AR curve: Total Revenue is: Total Revenue is: Profits are therefore:

Frank Cowell: Microeconomics Ex 4.13(2) Maximising profits FOC (MC = MR) yields: FOC (MC = MR) yields: So monopolist’s optimal output is: So monopolist’s optimal output is: From AR curve, price at optimum is: From AR curve, price at optimum is: Simplify this to: Simplify this to:   (clearly price > MC)

Frank Cowell: Microeconomics Ex 4.13(3) Question Method: Aggregate the CV for each consumer to define L. Aggregate the CV for each consumer to define L. Use marginal cost and monopolist’s equilibrium price to evaluate L Use marginal cost and monopolist’s equilibrium price to evaluate L

Frank Cowell: Microeconomics Ex 4.13(3) Evaluating loss Use definition of CV with p 1 ' = c: Evaluate L at p 1 = 2c: Firm’s profits are: Clearly L > profits

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

Frank Cowell: Microeconomics 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:

Frank Cowell: Microeconomics 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

Frank Cowell: Microeconomics Ex 4.13: Points to note Aggregate welfare loss is found from individual CV Unregulated monopoly makes profits smaller than losses top consumer Regulation causes monopoly to behave like competitive firm