Economic Behaviour of Household: Theory of Time Allocation (Gary Becker)

1. Economic Behaviour of Household: Theory of Time Allocation (Gary Becker) Dwini Handayani

2. Two time uses in neoclassical economics: leisure market work (labor) Three time uses in the New Homes Economics: leisure market work (labor) household production

3. NEO CLASSICAL ECONOMICS

4. Labor Supply : Theory and Evidence • Labor supply decisions can be roughly divided into two categories: • Decisions about whether to work at all, if so, • how long to work. • (2) Decisions about the occupation or general class • of occupation in which to seek offers and the • geographical area in which offers should be • sought.

5. 2. A Theory of The Decision to Work • The decision to work is ultimately a decision about how to spend time. Spend time in pleasurable leisure activities Use time to work (working for pay) • The discretionary time we have (24 hours – time spent eating and sleeping) can be allocated to either work or leisure. Demand for Leisure Supply of Labor.

6. Basically, the demand for a good is a function of three factors: • The opportunity cost of the good. • One’s level of wealth. • One’s set of preference. The demand（D） for a normal good can be characterized as a function of opportunity cost（C）and wealth（V） D = f（C, V）

7. Where f depends on preferences. Demand for Leisure: (1) The opportunity cost of an hour of leisure is very closely related to one’s wage rate. For simplicity, we shall say that leisure’s opportunity cost is the wage rate. (2) Economists often use total income as an indicator of total wealth, since the two are conceptually so closely related. Demand for leisure function becomes DL = f（W, Y）

8. (1) If income increases, holding wages（and f）constant, the demand for leisure goes up. If income increases（decreases）, holding wages constant, hours of work will go down（up）. Income effect on hours of work is negative. Income Effect =  w<0

9. (2) If income is held constant, an increase（decrease）in the wage rate will reduce（increase）the demand for leisure, thereby increasing（decreasing）work incentives. Substitution effect on hours of work is positive. Substitution Effect =  Y>0

10. Both Effect Occur When Wages Rise Income effect: For a given level of work effort, he/she now has a greater command over resources than before because more income is received for any given number of hours of work. Substitution effect: The wage increase raises the opportunity costs of leisure, and thereby increases hours of work.

11. If income effect is dominant, the person will respond to a wage increase by decreasing his/her labor supply. Should the substitution effect dominate, the person’s labor supply curve will be positively sloped. Wage Backward-bending W* Desired hours of work

12. 3. A Graphic Analysis of the Labor-Leisure Choice Two categories of goods: Leisure（L）and Money Income ( M ) Since both leisure and money can be used to generate satisfaction, these two goods are to some extent substitutes for each other. M Indifference Curve: A curve connecting the various combinations of money income and leisure that yield equal utility. A B IC2 C D IC1 L

13. Indifference curves have certain specific characteristics: • Any curve that lies to the northeast of another one is preferred to any curve to the southwest because the northeastern curve represents a higher level of utility. • Indifference curves do not intersect. • Indifference curves are negatively sloped. • Indifference curves are convex. • When money income is relatively high and leisure hours are relatively few, leisure is more highly valued than when leisure is abundant and income relatively scarce. • 5. Different people have different sets of IC’s

14. M M L L Person who place high value on an extra hour of leisure Person who place low value on an extra hour of leisure

15. The resources anyone can command are limited. Budget constraint reflects the combinations of leisure and income that are possible for the individual. M The slope of the budget constraint is a graphic representation of the wage rate. Wage rate = OE/OD E L 0 D

16. Note: Full income = wage rate * T →It represents the maximum attainable income. M At point B: MUL/MUM>W or MUL>W*MUM L should increase At point C: MUL/MUM<W or MUL<W*MUM L should reduce, or H should increase E B A* IC2 IC* C IC1 • An indifference curve that is just tangent to the constraint represents the highest level of utility that the person can obtain given his or her constraint. L D IC2：impossible under current condition IC1：possible, but higher level of utility can be attained IC*：utility-maximized level A* ：utility-maximization point

17. The Decision Not to Work What happens if there is no point of tangency? M The person’s IC are at every point more steeply than the budget constraint. Pt. D is not a tangency point. There can be no tangency if the IC has no points at which the slope equals the slope of the budget constraint. E L D At this point（D）the person chooses not to be in the labor force.

18. Recall: Leisure Work Analysis (4) • Income effect income real naik, makin kaya maka mampu untuk meningkatkan Leisure. 2. Substitution effect income real naik, artinya harga leisure naik, mendorong untuk meningkatkan jam kerja Total effect: dalam keadaan normal akan meningkatkan jam kerja (SE>IE).

19. The Income Effect Nonlabor income: Even if this person worked zero hour per day, he/she will have this nonlabor income. M Note that the new constraint is parallel to the old one. →The increase in nonlabor income has not changed the person’s wage rate. E B A IC2 IC1 L D Pure income effect: The income effect is negative; as income goes up, holding wages constant, hours of work goes down.

20. Income and Substitution Effects with a Wage Increase The wage increase would cause both an income and a substitution effect; the person would be wealthier and face a higher opportunity cost of leisure. N1→N3: income effect → L↑, H↓ N3→N2: substitution effect →L↓, H↑ N1→N2: observed effect Substitution effect dominates. L↓, H↑ Income effect: Had the person received nonlabor income, with no change in the wage, sufficient to reach the new level of utility, he/she would have reduces work hours from N1 to N3.

21. N1→N3: income effect →L↑, H↓ N3→N2: substitution effect →L↓, H↑ N1→N2: observed effect Income effect dominates. L↑, H↓ Note: The differences in the observed effects of a wage increase are due to differences in the shape of the indifference curve. i.e., different preference.

22. Recall: Leisure Work Analysis (1) Max: U = u (C, L) ...1 St : PC = WH + V ...2 T = H + L ...3 (2) PC =WH + V C = (W/P) H + V/P (slope budget line =w/p)

23. Recall: Leisure Work Analysis (2) Maksimisasi: £ = u (C, L) + λ (PC- WT + WL –V) FOC: ∂ £/ ∂ L = MUL= λ W =0 ∂ £/ ∂ C = MUC = λ P =0 Jadi Optimum ketika: MUL / MUC = W/P (slope IC = slope BL)

24. Recall: Leisure Work Analysis (3) Keputusan jumlah leisure dan hours for work optimum saat : MUL / MUC = W/P Ketika upah naik, terdapat 2 effect: 1. Income effect (L ↑) 2. Substitution effect (L ↓)

25. Income and Substitution Effects with a Wage Increase The wage increase would cause both an income and a substitution effect; the person would be wealthier and face a higher opportunity cost of leisure. N1→N3: income effect → L↑, H↓ N3→N2: substitution effect →L↓, H↑ N1→N2: observed effect Substitution effect dominates. L↓, H↑ Income effect: Had the person received nonlabor income, with no change in the wage, sufficient to reach the new level of utility, he/she would have reduces work hours from N1 to N3.

26. N1→N3: income effect →L↑, H↓ N3→N2: substitution effect →L↓, H↑ N1→N2: observed effect Income effect dominates. L↑, H↓ Note: The differences in the observed effects of a wage increase are due to differences in the shape of the indifference curve. i.e., different preference.

27. Recall: Leisure Work Analysis (6): Backward Bending Supply

28. NEW HOMES ECONOMICS

29. Allocation of time (1) Becker (EJ, 1965) "A Theory of the Allocation of Time“ Becker wrote: households are "assumed to combine time and market goods to produce more basic commodities that directly enter their utility functions.“

30. Allocation of time (2) Becker’s Asumptions: • commodities (outputs) measurable • commodity (shadow) prices • constant returns to scale • single person households • no human capital

31. Theory of the Allocation of Time (3) Kegiatan individu/hh: • market production (work) • nonmarket production (household production) • Leisure

32. Asumsi: HH memaksimisasi utility U= U(Z1, Z2, ...., Zn) HH diasumsikan mengkombinasi time dan market goods: untuk memproduksi basic commodities (Zi) Zi = fi (xi, Ti)

33. Becker emphasize: • goods purchase are not immediate source of utility • to consume and satisfy utility also require inputs of HH member’s time → in producing final commodities that yields utility

34. Theory of the Allocation of Time (4) Dalam memaksimisasi utility, individu/hh dihadapkan pada kendala: • Waktu terbatas (T= time) • Sumber daya terbatas ( S= full income) yaitu 1. T= tm + ∑ti 2. y = ∑Pi xi

35. Theory of the Allocation of Time (5) • Full income is time and resources of HH to earn income (from work and nonlabor income). • Dalam makismisasi alokasi waktu: tidak hanya semata-mata mementingkan kerja, tetapi harus juga dialokasikan untuk kegiatan lain. • Kerja terus ? Tidak tidur ? Mana mungkin

36. Secara grafis

37. goods • To formalize this, define the household’s budget in terms of both • what they can produce for themselves, in home production home production possibilities frontier Slope = marginal product of labor in home production time Total time

38. Indifference curve: U = u(X,l) Slope = marginal rate of substitution of goods for leisure time goods Household utility is defined over goods and leisure time (as usual) w/P Time

39. goods The essence of the model is that an individual will work at home w/P as long as the marginal product of labor in home production exceeds the marginal return to market work (w/P). less steep Steeper than w/P Work at home

40. goods And will work in the market until the return to labor (w/P) is just exceeded by the marginal rate of substitution for leisure w/P market work Work at home

41. When wages for market work are relatively high goods all work time will be in the market, for a cash wage w/P And the rest will be leisure time Time Market work

42. When wages for market work are relatively low : w/P goods And the rest will be leisure time Time all work time will be in home production

43. The familiar case: A little time in home production, high returns to market work full-time market work, and leisure time. goods low productivity in most home production leisure market work home production

45. Secara matematis

46. Secara Matematis: Makimisasi Utility: U= U(Z1, Z2, ...., Zn) ...(1) Subject to: 1. T= tm + ∑ti ...(2) 2. y = ∑Pi xi ...(3) Dimana 3. Zi = fi(xi, ti) ...(4) 4. Z = g (Zi,...,Zm) ...(5) (sederhanakan kendala)

47. T= tm + ∑ti tm= T- ∑ti ...(1a) (2) y = ∑Pi xi = w. tm + V (1a) & (2) ∑Pi xi = w. tm + V ∑Pi xi = w. (T- ∑ti) + V ∑Pi xi + w . ∑ti = w.T + V (full income=S)

48. Problem Maksimisasi Menjadi: Maksimisasi U = u( Z1,...., Zn) Dimana Zi = fi (xi, ti) Subject to: S = ∑Pi xi + w . ∑ti

49. Problem Maksimisasi ʆ =u[ Z1, Z2,....,Zm]+λ [ S- ∑Pi xi - w .∑ti ] .......(a)

50. Problem Maksimisasi ʆ =u[ Z1, Z2,....,Zm]+λ [ S- ∑Pi xi - w .∑ti ] .......(b)