Frank Cowell Microeconomics November 2006 Exercise 3 4

Frank Cowell: Microeconomics November 2006 Exercise 3. 4 MICROECONOMICS Principles and Analysis Frank Cowell

Ex 3. 4(1) Question Frank Cowell: Microeconomics n n purpose: to derive competitive supply function method: derive AC, MC

Ex 3. 4(1) Costs Frank Cowell: Microeconomics n Integrate MC to get total cost n Divide by q to get average costs n Differentiate to find minimum AC at n Average costs at this point are n If price is above this level find equilibrium where price = MC: n Solving this we get

Ex 3. 4(1): Firm’s supply curve Frank Cowell: Microeconomics §Average cost §Marginal cost §Supply of output a+bq §Relation between price and output Pp F 0/q+a+0. 5 bq q p a q*= —— b q

Ex 3. 4(2) Question Frank Cowell: Microeconomics n n purpose: to derive monopolist’s solution method: derive AR, MR

Ex 3. 4(2) Monopolist’s equilibrium Frank Cowell: Microeconomics n Given the demand curve total revenue is Aq ½Bq 2 n So, MR is n Monopolist’s FOC (MR=MC) n Solving for q we get n And from this we have

P Ex 3. 4(2): Monopoly output and price Frank Cowell: Microeconomics §AC and MC curves §Demand (average revenue) §Marginal revenue a+bq §Profit-maximising output §MC and price at q** p** F 0/q+a+0. 5 bq c** A 0. 5 bq A bq q** q

Ex 3. 4(3) Question Frank Cowell: Microeconomics n n purpose: to derive modified monopoly solution method: derive modified AR, MR – watch out for discontinuity!

Ex 3. 4(3) Regulated monopolist Frank Cowell: Microeconomics n Price ceiling alters the effective demand curve So AR is now: n Multiply by q and then differentiate to get MR: n MR is discontinuous, exactly where AR is kinked Effect of price ceiling depends on position of MC relative to this discontinuity n n

Ex 3. 4(3): High price ceiling Frank Cowell: Microeconomics §AC and MC curves §Demand (average revenue) §Marginal revenue §Profit-maximising output §MC and price at q** p** A high ceiling has no effect on equilibrium § c** q

Ex 3. 4(3): Low price ceiling Frank Cowell: Microeconomics §AC and MC curves §Demand (average revenue) §Marginal revenue §Profit-maximising output p** A low ceiling yields equilibrium at reduced output q 0 §price = MC = price ceiling § c** q 0 q** q

Ex 3. 4(3): Medium price ceiling (i) Frank Cowell: Microeconomics §AC and MC curves §Demand (average revenue) §Marginal revenue §Profit-maximising output p** A medium ceiling yields equilibrium at increased output q 0 § c** q 0 q

Ex 3. 4(3): Medium price ceiling (ii) Frank Cowell: Microeconomics §AC and MC curves §Demand (average revenue) §Marginal revenue §Profit-maximising output p** Again, a medium ceiling yields equilibrium at increased output q 0 § c** q 0 q

Ex 3. 4: Points to remember Frank Cowell: Microeconomics n n Make good use of a diagram to “see” the problem Re-use the solutions u u n one part of the problem… …helps to build the next. Don’t be fazed by the presence of a discontinuity u everything is nice and regular either side of it.