Question

rick purchses two goods food and clothing

1. Rick purchases two goods, food and clothing. He has a diminishing marginal rate of substi- tution of food for clothing. Let z denote the amount of food consumed and y the amount of elothing. Suppose the price of food increases from P to P (> P). On a clearly labeled graph, illustrate the income and substitution effects of the price change on the consumption of food. Do so for each of the following cases: (a) Case 1: Food is a normal good. (b) Case 2: Food is neither normal nor inferior good. (e) Case 3: Food is an inferior good, but not a Giffen good. (d) Case 4: Food is a Giffen good.

Answer 1

a. Case 1: Food is a normal good. Given the iucrease in the pice ofx, we expect to see e following etfects: Sbstitution Ettect Income Effect telativel eistively less expensive As a resulr, Rick substinures awar from xin faver of is epeeted in substitution effect coluaa This etable by a dowu sow fo x und an up aow fou yin the Moreover, the increase in the price of xedced Rick's purchasing power. Since aud ye both ucal goods being a noal good is giveu by he poblembeing onochase less ofhoth xand u 1This is eoreseated in the table hr the down antoors in the income ettect cohumo. The following diagram gives us a graphical representation of the information presented in the table BL The ital csupou bundle is epeseted by point 4 which lies ou the iitial budget line BL The incease in the price of xcases the budget line shitt wards to BL The new cansumption bundle is represented br point C We then coustract point Bin oder to sepaate the substitution effect from the income effect The oveeut fiom 4 to Brepresents the substitution eflect Note that u the table, the movement fromB to Cshows both and y going at sggested down. b. Case 2: The income clasticiry demand for food is zero. In this case, wre expect to sec the following effocrs: Substitution Effret Income Effect Once apin, because the price of x inceased, Rick substitutes away from xin favor of y This is represented in the table by a down anow for x aud au up amow for y in he sultitutiou effect colu Howeve, he foti he coe efect culun lus cluged Siuce he demand for xis zero, rhe redction in Rick's purchasing power income clasticite T pts * e or n the income contining to assume that y is a nomal good) The follow diagau gives us a gaplical repesentation of the infomation peseed in te able BL BL. As before, the initial consumption bundle is represented by point A, and the new consumption bundle is tepesented by point C. Poit Bis constructed in ordes to separate the substitution cffect from the income cffect.

The movement from 4 to B represents the substitution effect, and as suggested by the table, we observe x going down snd y going up. The movement from B to C Iepresents the income effect. since the income elasticity of demand for xis zero. On the other hand, we do observe y going down since yis assumed As suggested by the table, we observe no change in e a notmal good c. Casc 3: Food is an inferior good, but not a Giffen good. In this case, we expect to see the following effects: Substitution Effect Income Effect Once again, because the price of xincreased, Rick substitutes awar from xin favor of y. Moreover, the reduction in Rick's purchasing power reduces his demand for) (a nomal good). What is new is an nleio good; that is, the eduction itn Rick's puchasing hase ore . This is represented by the up arrow for xin the income elect column. The following diagram gires us a graphical representation of the information presented in the table BL ,and the new As hefore, the initial consumption undle is epresented by point consumption bundle is represented by point C Point B is constmcted in order to separate the sulbstitution effect fiom the income eflect The movement from A to B represents the substitution effect, and as suggested by the table, we observe x going down and y going up. The movement from B to C s suggested by the table, we observeygoing up (since 1epresents the income eflect. yis assumed infeior good) be a normal good) and xgoing down (since xis assumed be an The last thing to take note of is that the diagram indicates that xis not a Giffen good. The diapcam indlicates that the income effect is not stong enough substitution effect; that decrease in xgoing from A to B dominate the the increase inx going from B to Cis amaller than the The last thing to take note of is that the diagram indicates that xis a Giffen good. The diagram indicates thst the income effect domnates the substitution effect; thst the increase in x going from B to Cis larger than the decrease in x going from A to 15