2. Econ 203: Topic 7 The choice between consumption and leisure revisited The Slutsky formulation Reading: Varian Chapter 9 pages 166-171 and 174-175

3. 0 X0X0 A Y X Y0Y0 P x X= P x X c + P y Y c

4. 0 R0R0 A Earnings Leisure Leisure = R Total hours = T C0C0

5. 0 R0R0 A Earnings plus Money (M/P) Leisure C0C0

6. 0 R0R0 A Earnings plus Money Price of leisure rises from W 0 to W 1 Budget constraint swivels in Leisure C0C0

7. 0 RARA A Earnings plus Money But the reward for work also rises shifting the BC out U1U1 Leisure

8. 0 RARA RDRD A D Earnings plus Money New Equilibrium at D U1U1 U2U2 Leisure What are the income and Sub effects here?

9. 0 RARA RDRD A D Earnings plus Money Moving income back to U 1 (Hicks) U1U1 U2U2 Leisure

10. 0 RARA RDRD A B D Earnings plus Money RBRB R A -R B is the Hicksian substitution effect {A-B on diagram}. U1U1 U2U2 Leisure Deriving equilibrium at new prices on U 1 we find point B.

11. 0 RARA RDRD A B D Earnings plus Money C RBRB Can also look at what demand would have been on original leisure- price-rise line. That is point C. U1U1 U2U2 U0U0 Leisure

12. 0 RARA RDRD A B C D RCRC Earnings plus Money RBRB R B -R C is the standard income effect {Point B to C on the diagram}. U2U2 U1U1 U0U0 Leisure

13. 0 RARA RDRD A B C D RCRC Earnings plus Money RBRB R C -R D is the endowment income effect {Point C to D on the diagram}. U2U2 U1U1 U0U0 Leisure

14. Substitution Effect A -> B 0 RARA RDRD A B C D RCRC RBRB U2U2 U1U1 U0U0 Leisure

15. Income Effect B -> C 0 RARA RDRD A B C D RCRC RBRB U2U2 U1U1 U0U0 Leisure

16. Endowment Effect C -> D 0 RARA RDRD A B C D RCRC RBRB U2U2 U1U1 U0U0 Leisure

17. Now we have a substitution effect from A to B, causing the number of hours of leisure worked to fall from R A to R B Next we have an income effect from B to C, causing the number of hours of leisure to fall from R B to R C Finally we have an ENDOWMENT effect from C to D, causing the number of hours of leisure to rise from R C to R D

18. Remember that we usually assume that leisure is a normal good. The rise in the price of leisure causes us to buy less of it (from R A to R B ). A rise in the price of any good makes us poorer, and since ‘real income’ is lower (ignoring the endowment effect) we buy less leisure (the fall from R B to R C ). But now if we take account of the endowment effect our total income has risen, since for every hour of work we actually do, our pay has increased, and so we will consume more leisure (the move from R C to R D ).

19. Get the idea! Good, because now we are ready for the nasty bit. The Endowment Slutsky Equation AAAGGGGHHH

20. Slutsky Endowment Effect Varian Ch 9 And Especially 9.7 - 9.9 & the Appendix

21. Terminology: I is Income M is Money or unearned income W is the nominal wage rate, (w real wage) P is the price level T is the total number of hours in the day R is the number of hours of leisure taken L is the hours of work done. c is our actual or real consumption of goods

22. The Endowment Slutsky Effect Our consumption of Leisure depends on the price of R (W) and our overall level of Wealth. We are endowed with M amount of Money and T units of Time. So our Wealth (I) is: I = M +WT = Pc+WR or c = (T-R)W/P +M/P which in real terms implies that c = (T-R)w +m, where w is the real wage rate and m is real money balances

23. The Endowment Slutsky Effect So R depends on w and I which is also a function of w. That is R[W, I(W)] So

24. The Endowment Slutsky Effect But if we differentiate I=M +WT with respect to W we get T

25. The Endowment Slutsky Effect What about the first term on the RHS? It is the change in R when Income cannot change -that is, it’s the usual Slutsky effect

26. The Endowment Slutsky Effect

28. Substitution Effect R A to R B Income Effect R B to R C Endowment Effect R C to R D or in other words, the overall effect is: the substitution effect (from R A to R B ), minus the usual income effect (from R B to R C ) plus the endowment effect (from R C to R D ).

29. The Endowment Slutsky Effect

31. Differentiating c = (T-R)w +m, with respect to the real wage yields

32. M/P T hours 0 Earnings plus Money Holdings R*R* C*C* U2U2 Hours worked when Free to Choose

33. M/P T hours 0 Earnings plus Money Holdings R*R* C*C* U2U2 But what if you have to work a 40 hour week minimum?

34. M/P T hours 0 Earnings plus Money Holdings R*R* C*C* U2U2 U1U1 Utility falls to U 1 and work and consumption rise

35. M/P T hours 0 Earnings plus Money Holdings R*R* C*C* U2U2 U1U1 Note if choose not to work, get U 0 but since U 1 is greater will prefer work. U0U0

36. M/P T hours 0 Earnings plus Money Holdings R*R* C*C* U2U2 U1U1 U0U0 But if like leisure more you have steeper U curves and so choose not working U 1 to work U 0

37. Exercise Topic 7 Bottom Line: Changes in w/p over the cycle will not induce much variation in hours worked However, changes in overtime rates will (pure substitution effect) Main effect will be on marginal individual making the work/no-work decision In particular for higher w/p people are more likely to make the effort to be in employment

38. W/PlSlS lDlD What are the implications of this for our Labour Demand & Supply diagrams?

39. W/PlSlS lDlD

40. lSlS lDlD l l l u lS’lS’

41. W/PlSlS lDlD l l l u lS’lS’

42. W/PlSlS lDlD l l l u lS’lS’

43. W/PlSlS lDlD l l l u lS’lS’

44. Non-Assessed test 1998/99

45. Non-Assessed test 1998/99 & Non-Assessed test 2000/1 Better, but still not very good

46. 203 Assessed test 0 10 20 30 40 50 <3030-3435-3940-4950-5960-6970-7980-8990-100 98/99 99/00