1. EC202: Worked Example #3.17 Frank Cowell April 2004
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2. WX3.17: part 1

3. WX3.17: part 1 y2
Larger value of A
RHS is positive y1

4. WX3.17: part 2

5. WX3.17: part 2 Profits are given by:
We must be on the transformation curve
Substitute in to get:
Maximise this with respect to y1 , y2

6. WX3.17: part 2 FOC are: …which gives us:
Substitute back in for maximised profits:

7. WX3.17: part 3

8. WX3.17: part 3 Utility of capitalists
Given the Cobb-Douglas utility function they spend equal amounts on the two goods

9. WX3.17: part 3 Utility of workers
They maximise this given the budget constraint:
This is equivalent to maximising

10. WX3.17: part 3 FOC is: which yields optimal labour supply:
So, from the budget constraint:

11. WX3.17: part 4

12. WX3.17: part 4
No stock of goods 1 or 2. Workers do not consume good 2. So Excess demands are:
Set EDs to get equilibrium:

13. WX3.17: part 4 From this we get: So equilibrium price ratio is From P:
Solving this we get:

14. WX3.17: part 5 Profits in equilibrium: Wages in equilibrium:
Profit/Wage ratio is independent of A.