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Exercise 3.4

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

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Exercise 3.4

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  1. Exercise 3.4 MICROECONOMICS Principles and Analysis Frank Cowell November 2006

  2. Ex 3.4(1) Question • purpose: to derive competitive supply function • method: derive AC, MC

  3. 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

  4. p  a —— b q*= 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 q

  5. Ex 3.4(2) Question • purpose: to derive monopolist’s solution • method: derive AR, MR

  6. 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

  7. Ex 3.4(2): Monopoly output and price P • 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**

  8. Ex 3.4(3) Question • purpose: to derive modified monopoly solution • method: derive modified AR, MR – watch out for discontinuity!

  9. 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

  10. 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**

  11. 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 q0 q**

  12. 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 q2 q0 q**

  13. 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**

  14. 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.

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