# Frank Cowell Microeconomics November 2006 Exercise 4 13

Frank Cowell: Microeconomics November 2006 Exercise 4. 13 MICROECONOMICS Principles and Analysis Frank Cowell

Ex 4. 13(1) Question Frank Cowell: Microeconomics n n 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) Frank Cowell: Microeconomics n n A natural monopoly requires that costs be subadditive Subadditivity implies the following u u u n n given an integer m > 1 C(w, q) < m. C(w, q/m) (see Ex 3. 1) In the present case costs are C 0 + cq Clearly m[C 0 + cq/m] = m. C 0 + cq > C 0 + cq

Ex 4. 13(2) Question Frank Cowell: Microeconomics Method: n Find monopolist’s AR from consumer demand using answer to Ex 4. 12. n Then use standard optimisation procedure

Ex 4. 13(2) Monopoly profits Frank Cowell: Microeconomics n Aggregate demand over N consumers using Exercise 4. 12 n Rearrange to get AR curve: n Total Revenue is: Profits are therefore: n

Ex 4. 13(2) Maximising profits Frank Cowell: Microeconomics n FOC (MC = MR) yields: n So monopolist’s optimal output is: n From AR curve, price at optimum is: n Simplify this to: u (clearly price > MC)

Ex 4. 13(3) Question Frank Cowell: Microeconomics Method: n Aggregate the CV for each consumer to define L. n Use marginal cost and monopolist’s equilibrium price to evaluate L

Ex 4. 13(3) Evaluating loss Frank Cowell: Microeconomics n Use definition of CV with p 1' = c: n Evaluate L at p 1 = 2 c: n Firm’s profits are: n Clearly L > profits

Ex 4. 13(4) Question Frank Cowell: Microeconomics Method: n Add bonus B into the expression for profits n Again use standard optimisation procedure

Ex 4. 13(4) Evaluating profits (again) Frank Cowell: Microeconomics n Profits including bonus are: n Value of bonus is: n Use demand curve to express this in terms of q: n So profits can now be expressed as:

Ex 4. 13(4) Evaluating profits (again) Frank Cowell: Microeconomics n n Take the expression for profits including bonus FOC for a maximum is again MR = MC: n Rearranging we get the value of optimal output for the regulated monopolist: n Use demand curve to find: n Clearly the regulated price = MC

Ex 4. 13: Points to note Frank Cowell: Microeconomics Aggregate welfare loss is found from individual CV n Unregulated monopoly makes profits smaller than losses top consumer n Regulation causes monopoly to behave like competitive firm n

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