Tutorial Exercises 4: Consumer Theory

Transcription

1 FB 00 ECONOMCS Tutrial Exercises : Cnsumer Thery Essential readings: Chapter.. Draw the indifference curve fr gds A and B if they are (a) (b) Perfect Substitutes: N matter hw much f gds A and B the cnsumer is cnsuming (that is, n matter at what pint we are n the indifference curve), whenever we take away a certain amunt f gd B frm the cnsumer, we can always cmpensate the cnsumer with the same amunt gd A t keep him/her n the same indifference curve. Perfect Cmplements: The cnsumer can cntinuusly increase the amunt f utility he derives frm gds A and B nly by increasing his/her cnsumptin f gds A and B in cnstant/fixed prprtins. Discuss the cnsumer equilibrium in these cases.. Sme restaurants ffer buffet dinner. Fr example, cnsumers pay a price f $00 and then can cnsume all they want. Shuld yu have a buffet dinner r have a regular dinner?. When a cnsumer buys a cup f cffee at Uncle Russ Cffee, he als receives a chp. Uncle Russ Cffer ffers a free drink fr the cnsumers wh have cllected chps n ther wrds, it is a buy get ne free prgram. Can yu benefit frm the prgram?. After the Sichuan earthquake in May, 008, huge amunts f dnatin were received frm the public in Hng Kng. While many f us cntributed in-cash dnatin, sme peple cntributed inkind r in-service dnatin. Fr example, sleeping-bags, prtective gwns, bk shelves, and mst ntably, vluntary medical supprts frm dctrs and nurses. Sme rganizatins recmmended peple t cntributin in-cash dnatin rather than in-kind dnatin. Why? Let s cmpare the difference between a dnatin f $000 and a dnatin f $00-wrth fd.. n-class discussin: Essay Questin Thery f Cnsumer

2 FB 00 ECONOMCS Suggested (Nt Restrictive) Answers. a) Perfect Substitutes Gd B (e.g. Purple $0 ntes issued by HKMA) 0 A BL Perfect Substitutes BL U U B U U 0 Gd A (e.g. Green $0 ntes) The tw gds must be viewed as the same, s diminishing marginal rate f substitutin is impssible. Fr example, any green $0 nte ffers the same utility as any purple $0 nte. As shwn in the figure, the typical cnsumer is always willing t trade a green $0 nte t a purple $0 nte at a cnstant rate (in this case, ne-fr-ne) while remaining equally well ff. Cnsumer equilibrium: f the relative price f gd A (slpe f budget line) is equal t the marginal rate f substitutin (slpe f the indifference curve), like BL, the budget line lies n tp f the indifference curve U. Therefre any basket n the budget line will be ptimal as all these baskets lead t the same level f utility. Hwever, if the relative price is nt equal t the MRS, like BL. n this case, Gd B is cheaper as the relative price f Gd B is / units f Gd A. The ptimal chice is at a crner pint A with units f gd B but n gd A. The highest attainable indifference curve is U. Facing tw perfect substitutes, a cnsumer will nly buy the cheaper ne. b) Perfect Cmplements U < U < U < U Gd B (e.g. Glasses Frame) The tw gds are perfect cmplements if they must be cmbined at a fixed prprtin t yield a certain utility. n this case, the desired prprtin f glasses frame t lens is :. Fr example, the cnsumer derives U satisfactin frm cmplete set f lenses and glasses frame, but gets n additinal U utility if he cnsumes extra glasses frame r U extra lens. A BL BL Cnsumer equilibrium: Given the budget line like BL, the ptimal Gd A (e.g. Lens) chice is pint A with glasses frame and lenses. The utility attained is U. Hwever, if the price f lens drps, the budget line changes t BL. Despite the fact that he can buy mre lens nw, he will nt buy mre lens because extra lens des nt generate mre utility fr him unless he can buy mre glasses frame. The ptimal chice MUST be a basket that the rati f glasses frame t lens is :.. Buffet Dinner Figure : Perfect Cmplements U < U < U Under nrmal pricing scheme, the budget line is BL.

3 FB 00 ECONOMCS f the cnsumer have a buffet dinner, he must pay the lump sum payment f $00 regardless f the number f dish cnsumed S, the maximum amunt f ther gd that ( $00) he can buy drps t. By paying $00, the price per dish becmes zer, the budget line becmes hrizntal. That is, BL. Whether the cnsumer will be better ff having a buffet dinner depends n his preference (indifference map). n this case, the cnsumer will be better ff having a buffet dinner and he will have mre dishes under the buffet pricing. Shw an indifference map f a cnsumer wh wuld find it better nt t have buffet dinner. Other gd (y) $ 00 E U E BL U 00 BL Fd (dish, f). Uncle Russ Cffee s Chps Prgram Other Gd (y) E E U U BL p c BL Cffee (c) Under nrmal pricing scheme, the budget line is BL.

4 FB 00 ECONOMCS With a buy get ne free prgram, the budget line desn t change fr cnsumptin f less than cups. After cnsuming the th cup, the budget cnstraint will expand by ne unit. Nte that the hrizntal segment als implies the price f the th cup is zer. Therefre, the budget line becmes L. Each cnsumer wn t be wrse ff with the scheme. Whether he will be better ff depends n his preference. n this case, the cnsumer will be better ff under the scheme and he will cnsume mre cffee frm Uncle Russ. Shw an indifference map f a cnsumer wh wuld nt benefit frm the scheme.. n-kind vs. n-cash Dnatin Other Gd (y) BL E BL E U U BL 000 p f 00 Fd (f) Originally, the budget line is BL. n-cash Dnatin: With a cash dnatin f $000, the budget line shifts utward in parallel frm BL t BL. The recipient must be better ff with the dnatin. Assuming fd is a nrmal gd, he will cnsume mre fd. n-kind Dnatin: With a in-kind dnatin f $000-wrth f fd, the recipient cannt cnsume mre ther gds. The maximum amunt f y he can buy remains at. Hwever, if he spends all his incme n ther gds, he can still cnsume $000-wrth f fd. The budget line, therefre, is kinked, i.e. L. The recipient must be better ff with the dnatin. Assuming fd is a nrmal gd, he will cnsume mre fd. S, which ne is preferred (Cmparing the tw types f dnatins)? Frm recipient s perspective: f the recipient has a preference as shwn in the abve diagram, the tw types f dnatin are indifferent. Hwever, if the recipient has a preference as shwn in the fllwing diagram, cash dnatin is definitely preferred. Frm dnr s perspective:

5 FB 00 ECONOMCS Sme dnrs may want t encurage the recipient t cnsume mre fd, rather than spending the dnatin n ther gds. n such case, in-kind dnatin is preferred. Other Gd (y) BL E E E U U U 000 p f BL BL 00 Fd (f)