MICROECONOMICS Principles and Analysis Frank Cowell Exercise 3.4 MICROECONOMICS Principles and Analysis Frank Cowell November 2006
Ex 3.4(1) Question purpose: to derive competitive supply function method: derive AC, MC
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
Ex 3.4(1): Firm’s supply curve Average cost Marginal cost Supply of output Relation between price and output a+bq P p F0/q+a+0.5bq q p a —— b q*= q
Ex 3.4(2) Question purpose: to derive monopolist’s solution method: derive AR, MR
Ex 3.4(2) Monopolist’s equilibrium Given the demand curve total revenue is Aq ½Bq2 So, MR is Monopolist’s FOC (MR=MC) Solving for q we get And from this we have
Ex 3.4(2): Monopoly output and price AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output a+bq MC and price at q** p** F0/q+a+0.5bq c** A 0.5bq A bq q q**
Ex 3.4(3) Question purpose: to derive modified monopoly solution method: derive modified AR, MR – watch out for discontinuity!
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
Ex 3.4(3): High price ceiling 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 q**
Ex 3.4(3): Low price ceiling AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output p** A low ceiling yields equilibrium at reduced output q1 price = MC = price ceiling c** q q1 q** q0
Ex 3.4(3): Medium price ceiling (i) AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output p** A medium ceiling yields equilibrium at increased output q2 c** q q** q2 q0
Ex 3.4(3): Medium price ceiling (ii) AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output p** Again, a medium ceiling yields equilibrium at increased output q0 c** q0 q q**
Ex 3.4: Points to remember Make good use of a diagram to “see” the problem Re-use the solutions one part of the problem… …helps to build the next. Don’t be fazed by the presence of a discontinuity everything is nice and regular either side of it.