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EC202: Worked Example #3.7

EC202: Worked Example #3.7. Frank Cowell April 2001. T his presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments To start the presentation select S lideshow V iew Show or click on icon below left.

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EC202: Worked Example #3.7

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  1. EC202: Worked Example #3.7 Frank Cowell April 2001 • This presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments • To start the presentation select Slideshow\View Show or click on icon below left. • Mouse click or [Enter] to advance through slide show

  2. WX3.7: part 1(a) . These are easy – parabolic contours Even easier – fixed money income First steps: • Sketch indifference curves • Write down budget constraint • Set out optimisation problem

  3. x2 . x1 WX3.7: part 1(a) Slope is vertical here We could have x2=0

  4. WX3.7: part 1(a) • Budget constraint: • Substitute this into the utility function: • We get the objective function: • FOC for an interior solution:

  5. WX3.7: part 1(a) • FOC for an interior solution: • Therefore, if positive amounts of the two goods are bought: • But this requires: • Otherwise x2=0 and we get x1 from the budget constraint.

  6. WX3.7: part 1(a) • Demand functions:

  7. WX3.7: part 1(a) • Maximised utility gives us the indirect utility function: • Otherwise:

  8. WX3.7: part 1(a) For case where both goods are consumed • For the cost function use the relation u=V(p,M) • … and solve for M:

  9. WX3.7: part 1(b,c) . Method: • Use C function to write down CV • (Equivalently use V function to write down CV) • Check income effects

  10. WX3.7: part 1(b,c) • Compensating variation is • But demand for good 1 has zero income effect • So CV = CS = EV in this case

  11. WX3.7: part 2(a) . Method: • Find monopolist’s AR from consumer demand using part 1. • Use standard optimisation procedure

  12. WX3.7: part 2(a) • Aggregate demand over N consumers using part 1: • Rearrange to get AR curve: • Total Revenue is: • Profits are therefore:

  13. MC = MR WX3.7: part 2(a) • FOC: • Optimal output: • From AR curve, price at optimum is: Price > MC • …simplified:

  14. WX3.7: part 2(b) . Method: • Aggregate the CV for each consumer to define L • Use marginal cost and monopolist’s equilibrium price to evaluate L

  15. WX3.7: part 2(b) • Use definition of CV with p1´ = c • Evaluate L at p1 = 2c

  16. WX3.7: part 2(c) . Method: • Add bonus B into the expression for profits • Again use standard optimisation procedure

  17. WX3.7: part 2(c) • Profits are now: • Value of bonus is: • Expressed in terms of quantity: • So profits become:

  18. WX3.7: part 2(c) • FOC: Price = MC • Resulting equilibrium:

  19. WX3.7: Points to note • The fact that indifference curves touch the axis does not cause any great problem • Aggregate welfare loss is found from individual CV • Regulation causes monopoly to behave like competitive firm

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