Question

John’s utility function is represented by the following: U(C,L) = (C-400)*(L-100), where C is
expenditure on consumption goods and L is hours of leisure time. Suppose that John receives
$150 per week in investment income regardless of how much he works. He earns a wage of $20
per hour. Assume that John has 110 non-sleeping hours a week that could be devoted to work.
a. Graph John’s budget constraint.
b. Find John’s optimal amount of consumption and leisure.
c. John inherits $300,000 from a relative which gives him $288 per week in additional
investment income. How does this change his hours of work decision? (Calculate C and
L). Is there an income and/or substitution effect? Explain.
d. Now suppose John’s wage increases to $50 per hour but he now still receives only $150
per week in investment income (no inheritance). Find his optimal amount of
consumption and leisure. Is there an income and/or substitution effect? Explain what
we can say about the relative magnitudes, if anything.

Answer 1

UCC, L) (c-400) CL-100 Assumiry mindlaire pe1 Budget constoan C=20 [110-L] +150 teums o [Huu17 C+ 20 L 2350 optfmal bimolle (c-400) CL-100 MRS JulaL du/dc 20 1 Siope of Budget conatraint Optimal eondibon C-400 L-100 20= Subir'tute in 1get 7 L=3150 96.75 39 50 40L1 = (i0 x21s1600 X on97xg)= C= 58.15 35 LIC) 7 I10-98.75-11.25 R Labowr kowrs = pen week eonsumpho'r [C+20L=2350 Budper Condt aaint 2350

Neo Budget constrain 110-L7+150 +288 C= 20 2638 Ct 201 Substitute Pn get we 40L 2638 1600 L =4238105. 15 40 = 20x423 81G00 40 C C= 519 labar houus of oonk 110-105.95 4.05 lako s hours Palls puom 1.25 to .0 Juat uere is no &ubstitution effee. h's aucansu thuw no nge inoage rate but chmge in Non-labosu Inome Jhere s Income effeet which is computed as Incomu effest for luswe -105,95-g8. 757. 2 519-375=144 Income effeet for conoimption or Both lho & consumption ueome effeet s pautive

udget constrain C =50 L 110-L]+ 150 50L+ C = 5650 Stopeof -50 Budget Condtraint Neo Optimal conditfon 8 50= C-400 L-10 0 50L-5000 C-400 C = 50L 4600 get i L Substitute 7 Pn (6 we 10a.S - 5650 +24 600 100L C- 50 X 10250 100 4600 = $25 la=labor housrs fr Income &Bubsituion Effect Entfal hoage rate Coo) 0-102. -7,S 1oeek [ eg1 50 [en 20 neo oage rate LW 11,25 labor1 Substi'tution effeet A m 4 h9) C309.(l.25 2labor hours A m Am 33 7.S

income motAm 2350+337.5 neuo 2687.5 voge Aate mi- wo20 New constrafnt 2687.8 20L+0 Surstitute in 4OL=2687.S41600 L-4287.S-107.19 40 C20 X 4283.1600 40 PLom C =S4.3.75 So optimal LTCt) C107 /9,543.75) at wo & nuo ineome is 110-107.19 - 2.8 Laborr 11.25-2.8/-8.44 Substi tutfon effeet 1-l2 er-ls= 2.81 -7S=-4.6I Ineom effer Substitution effeer s positive &Tneimy effeet ngative