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Analyzing Competitive and Monopolist Supply Functions in Microeconomics

This exercise outlines the process of deriving competitive supply and monopolist solutions in microeconomics, focusing on methods to ascertain Average Cost (AC) and Marginal Cost (MC). It includes steps to integrate MC for total cost, split into AC, differentiate for minimum AC, and establish equilibrium price conditions. Additionally, it explores monopolist pricing and adjustments due to price ceilings, highlighting demand curves, marginal revenue, and the impact of ceilings on output. Finally, it emphasizes the importance of diagrams in understanding economic problems.

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Analyzing Competitive and Monopolist Supply Functions in Microeconomics

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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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