Frank Cowell: Microeconomics Exercise 3.4 MICROECONOMICS Principles and Analysis Frank Cowell November 2006

Frank Cowell: Microeconomics Ex 3.4(1) Question purpose: to derive competitive supply function purpose: to derive competitive supply function method: derive AC, MC method: derive AC, MC

Frank Cowell: Microeconomics Ex 3.4(1) Costs Integrate MC to get total cost Divide by q to get average costs Differentiate to find minimum AC at Average costs at this point are If price is above this level find equilibrium where price = MC: Solving this we get

Frank Cowell: Microeconomics Ex 3.4(1): Firm’s supply curve q q P a+bq F 0 /q+a+0.5bq p  a —— b q*= p   Average cost   Marginal cost   Supply of output   Relation between price and output

Frank Cowell: Microeconomics Ex 3.4(2) Question purpose: to derive monopolist’s solution purpose: to derive monopolist’s solution method: derive AR, MR method: derive AR, MR

Frank Cowell: Microeconomics Ex 3.4(2) Monopolist’s equilibrium Given the demand curve total revenue is Aq  ½Bq 2 So, MR is Monopolist’s FOC (MR=MC) Solving for q we get And from this we have

Frank Cowell: Microeconomics q Ex 3.4(2): Monopoly output and price A  0.5bq P q** p** c** A  bq a+bq F 0 /q+a+0.5bq   AC and MC curves   Demand (average revenue)   Marginal revenue   Profit-maximising output   MC and price at q**

Frank Cowell: Microeconomics Ex 3.4(3) Question purpose: to derive modified monopoly solution purpose: to derive modified monopoly solution method: derive modified AR, MR – watch out for discontinuity! method: derive modified AR, MR – watch out for discontinuity!

Frank Cowell: Microeconomics Ex 3.4(3) Regulated monopolist Price ceiling alters the effective demand curve So AR is now: Multiply by q and then differentiate to get MR: MR is discontinuous, exactly where AR is kinked Effect of price ceiling depends on position of MC relative to this discontinuity

Frank Cowell: Microeconomics q Ex 3.4(3): High price ceiling q** p** c**   AC and MC curves   Demand (average revenue)   Marginal revenue   Profit-maximising output   MC and price at q**   A high ceiling has no effect on equilibrium

Frank Cowell: Microeconomics q Ex 3.4(3): Low price ceiling q** p** c**   AC and MC curves   Demand (average revenue)   Marginal revenue   Profit-maximising output   A low ceiling yields equilibrium at reduced output q 0   price = MC = price ceiling q0q0

Frank Cowell: Microeconomics q Ex 3.4(3): Medium price ceiling (i) q** p** c**   AC and MC curves   Demand (average revenue)   Marginal revenue   Profit-maximising output   A medium ceiling yields equilibrium at increased output q 0 q0q0

Frank Cowell: Microeconomics q Ex 3.4(3): Medium price ceiling (ii) q** p** c**   AC and MC curves   Demand (average revenue)   Marginal revenue   Profit-maximising output   Again, a medium ceiling yields equilibrium at increased output q 0 q0q0

Frank Cowell: Microeconomics Ex 3.4: Points to remember Make good use of a diagram to “see” the problem Make good use of a diagram to “see” the problem Re-use the solutions Re-use the solutions  one part of the problem…  …helps to build the next. Don’t be fazed by the presence of a discontinuity Don’t be fazed by the presence of a discontinuity  everything is nice and regular either side of it.