1. EC202: Worked Example #3.16 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
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2. WX3.16: part 1 x 1 2 A B D C
These four sets of indifference curves have the same structure as the isoquants in class 1

3. WX3.16: part 2 - problem
Step 1: set up the Lagrangean:

4. WX3.16: part 2 First-order conditions: Solve to get:
Offer curve is a vertical line at 10a

5. WX3.16: part 3 Points to watch:
Use your knowledge of the “shape” of the solution
For example we can get the solution to type A by adapting part 2
Types B-D follow by using the diagrams in Part 1

6. WX3.16: part 3, type A x2 20
We can use the demand function from part 2. Income is 20 now (instead of 10r) so solution must be:
20[1-a] x1
Offer curve is horizontal line at 20[1-a]

7. WX3.16: part 3, type B x2 x'
Solution must be on one or other axis unless r=b:
indifference curve b x1
x''
Offer curve is line segment with kink at x''

8. WX3.16: part 3, type C Solution must be on one or other axis:  g
Offer curve is blob at x' and line segment from x''

9. WX3.16: part 3, type D x2
Solution must lie on corner of the indifference curve where x2=dx1. Using this fact and the budget constraint x2+rx1=20 we have: d x1
Offer curve is line through the all the corners

10. WX3.16: part 4
Again we can re-use previous results, this time from parts 2 and 3

11. WX3.16: part 4, solution Draw the Edgeworth box Offer curve for type 110
Draw the Edgeworth box O2
Offer curve for type 1
Offer curve for type 2A 20
r=3 O1

12. WX3.16: part 4, solution (cont)
Offer curve for type 1 O2
Offer curve for type 2B
r=3 O1

13. WX3.16: part 4, solution Offer curve for type 1
Offer curve for type 2D
r=3 O1

14. WX3.16: part 5 Look at the box again Offer curve for type 2C
Will there be a solution? O1