Question

Problem 3 Alan's utility function for consumption (C) and leisure time (1) is U(C,1) = 2C1/2 + 1. Each week, Alan has a time endowment of 120 hours that he can devote to work (N) or leisure time (7). The unit price of C is $1 while the unit wage rate is w. Alan also earns A dollars per week of non-labor income. a) Write the expression of Alan's budget constraint. b) Find Alan's optimal combination of consumption and leisure time as a function of the wage rate w and of his non-labor income A. c) Does a higher wage push Alan to work longer hours or shorter hours? Show your work. d) Why do different workers respond differently to wage raises with some increasing their hours worked and others cutting hours worked? Suppose Alan won the Mega Million Lottery and his non-labor income increased. e) After winning the lottery, would he work longer or shorter hours? Justify your answer. f) After winning the lottery, would he decide to drop out of the labor force? Clearly explain? g) After winning the lottery, would Alan consumption (C) increase, stay the same or drop? Justify your answer. h) Does Alan consider leisure time a normal good or an inferior good? Justify your answer. .1.1. 1

Answer 1

Problem - 3. 0(0,0) = 210 + L. endowment - 120 Hours, wage date = w Price of consumption = 18 non Labor income =A @ money income = wage income + non waige income = 120 W + A equation of Budget construint Leisure + consumption - money income wht 1.C = 120 W + A Wht c = 120wt A Constraint. - (b) equilibrum condition MRS= MRE muc = Pc MOL El- To tc - sc = w c= w²

Budget constraint and from (i) wet c = 120w + A c= ² What w²= 120w +A w (l+ wj = 1200 + A (Low) = 120+ A =) L = 120+ A -w. W = L = 120wt A-w2 working hour (N) = 120 - (120w+ A-w²) w = 120w-120w - A tw² w N = Woo - W² A w w C= wz -> = (= (100+ Aw2 )? 1206+ A-w²121

C). as wage increase from w to w' That is w'sw. N = W²A when wage rate increases There are two effects that Leads to change in dabor Supply (1) se eyject (Substitution effect ). () IE (inome eyject) Substitution effect: ww wage rate increases from w tow' The Leisure becomes more exiensive o Than Previous, So Leads To increase in Labor Supply (or cookers will work more ). individual Income effect as wage rate increases, wage income increases Leads to Weapol individuals to cooral less and & Consume more, so individual works Shorter Case -I SEJIE, Alan work Longer hours.

Case-2. TE> SE 0227 Alan to work Shorter Hours- Case-3 TEASED Case-3 TE = SE No change in wook (d) different workers Respond differently to wage nise Because for different persons have different fre Jerences and that deads to different magnitude of Substitution and income ej Ject. working hours. - (e) N = w²A (Labor Supply Curve). - as A increases from A to A' where A'ZA. - So N = W²A > N=w² A So work shorter W W If in coords as A increases from A to A due to how labor in come with same level ofw, Alan wow want to work Less, So Labor supply decreases. (9) From (1) c- (120 w + A-w²2 A'DA C will increase from c toch where c'= (120w + Al-w2 ² w

in words, an increase in hon dabor income (A), Leads To Consumer The Alan To increase his Consumption Because a non-Labor income (A) will devoted To both Consumption and Leisure. (ho Since increase in non Labor income will devoted to both consumption and Leisure. as hon Labor income (that is after wining lottery) Leisure is also increase. So, Leisure is quo normal good you Alan. Justification. = 120 w+ A-w² W with AJA 1 = 1200 TA-W²> 1200 + A-w² - L W