1. EC202: Worked Example #3.18 Frank Cowell April 2004 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. WX3.18: part 1 WX3.13

3. WX3.18: part 1 Method: Sketch indifference curves Define offer curves Characterise utility maximisation for each party Sketch equilibrium Always useful for a quick view of the problem

4. WX3.18: part 1 MRS Utility function Person A Person B

5. WX3.18: part 1 We could have x 1 =0 Person a’s indifference curves

6. WX3.18: part 1 Person b’s indifference curves Constant MRS

7. WX3.18: part 1(a) Using a’s budget constraint: Set a’s MRS equal to price  … …to get a’s demand for good 1: …we get a’s demand for good 2 : Offer curve is locus of points where MRS = price. So… Offer curve

8. WX3.18: part 1(b) A sketch of Competitive equilibrium x1x1 x2x2 D E

9. WX3.18: part 1 Equilibrium is where common tangent to a and b indifference curves passes through initial endowment Clearly equilibrium price is  b So we have And a’s offer curve gives the equilibrium allocation We must have  a >  b Otherwise no trade We must have  a >  b Otherwise no trade

10. WX3.18: part 2 Method: Model new opportunity for person b Build in reaction of person a Solve the optimisation problem for person b

11. WX3.18: part 2 Given that b controls the price, he can determine his consumption as what is left over from a’s (price-taking) behaviour. Utility is: Substitute in a’s offer curve Maximise b’s utility by differentiating with respect to  : Putting this equal to zero we can see that  >  b. Person b’s consumption of good 1 Person b’s consumption of good 2

12. WX3.18: part 3 Method: Model new budget constraint for person a Solve for a’s reaction to fee and price. Model new opportunity for person b Build in reaction of person a Solve the optimisation problem for person b

13. WX3.18: part 3 New budget constraint for person a just reduces his endowment by F (for positive purchases) So optimal consumption of good 2 must be:

14. WX3.18: part 3 For a reservation utility is So b can set F such that a gets no more than reservation utility:

15. WX3.18: part 3 b’s utility is now Differentiating we get Substitute in a’s response: Putting this equal to zero we get  =  b. Clearly efficient!

16. WX3.18: part 3 A sketch of exploitative equilibrium (H) x1x1 x2x2 D H

17. WX3.18: Points to note Inspecting indifference curves immediately gives you the “shape” of the competitive equilibrium Simple monopolistic manipulation of price forces price up and is inefficient Allowing the monopolist to set an entry fee produces an efficient (but exploitative) solution.