Question

Suppose Peggy consumes only two goods, gasoline and cigarettes. Her income is $120, the price of cigarettes per pack is $4 and the price of gasoline per gallon is $2. Currently, she consumes 40 gallons of gas at optimal level.

a) Sketch the following budget lines. Be sure to show how you calculated the slopes and end points. (Put gas on the X axis.).

b) What is optimal level consumption of cigarettes for Peggy? Use an arbitrary convex indifference curve, indicating the current consumption combination is optimal.

c) If the government imposes a sales tax of $1 per unit on gasoline, Peggy will consume 28 gallons of gas. Draw the new budget constraint and the new optimal basket. Be sure to show how you calculated the slopes and end points. (Put gas on the X axis.).

d) What is optimal level consumption of cigarettes for Peggy? Use an arbitrary convex indifference curve, indicating the current consumption combination is optimal.

Answer 1

Suppose peggy consines only two giods gasoline (a) and cineraltis(C).Hu in come (m) is $ 120, o Price of ligeraltes pu Pack ic. Pc = $4 and Price of gasoline Pn gallon is $2 pe. PGI 2 Hunce, Hn budget constraint est to = c Pet Pa a) 120= 4e ti 2 Gunn a t Ics Scehned with neath 1202 20 + 40. eit mi a prima det at Thscamer

azek peggy sp and buys no cigual anis and cigual intu apt o 7 Substituting gay spinds her entire income on gusi no cigualt is then if we put gas on the x rigualts on the y - anis, then the horizontal ant of the budget line will be found by iftiting C=0 in the budgit constant p ice, 20-24 + 400 66001 1 gb peggy spends her entire e 4 spinds her entire income Pintical in ancept of the budgit round by o substituting 420 Hince, o 20 210 +4C on cigualty then line will be the budgit constrait a D ) C 30 و از د ها به بعد 45 در باره ی آن و ارز Also the slope of the budget line (absolute value] Hace by Joining horizontal We can get the budget line 22 liquattu ( C V MMVO B louso - PC 4 2 and vutical inancept, AB ou, Avele ادا زاری بوده که در . 80 درزی ای (درج در يرد الله له : دوا ہے ، ان كان ا ة ) - اد ی برین 30 * SINE SUGI Orol ICI 28 30g HD Senedi CamScanner

LA NO 2003 292 NO I H Now Ngobtimal's Consumptonari amb tonluvul 06 K asoline: * 40 Jallons gallons 60 an in the budg it constant 1 Substituting, ax = 40 We get: - 120=29* to HC*) 120=2(40) +40* HONDA CX9 D SUO! Dessut :10 - Online Hmce, optinial levil of Consmption of Surah flignally for Peggy u 10 packets of 2) P Hmce_Optimal love Cigualty for 71 C Liquadro 001 s Hunce the indifference cmue Ic, will be I would tauant to the al budgit line AB at the A. 1 1 optimal consmeton bundle cat,c* 40, ID <br ein von P UNLI i I Now, if the govunment imposu a sales I tan of 41 pm unit of gasoline, then the current Price of gasoline will be Da =912+1) = $ 3 Now, the budg it constraint will be? 120= 3ut 40 Il Now, it Peggy spends entire in come on gas Cu) The then horizontal intucept of the budget line will olla 120 = 39+4.10). IN) Rod o G = 40 Scanped with Cam Scanner

- Peggy spuds her entire in come on ciguralts (e Then the vätical in tucept of the budg it line will . Lbc. 120 3(0)74 C S S AC BOINV209 Ince the budget line will rotaty' in word from Bol to ABIN 22 Jagod ante Cabsolute Value) Now slope of the budget - constraint 4 Ta Now Peggy consmes 28 gallous of gas Substituting a= 281 in the budg it, Constaint we get 120313(28). + -1C* LINE Hunce now op t'mal for Reggy is is a level of consimption of igualtes packs of cigualty Lona no) I And the new indiftuence couc (I (2) will be tangent to the budg it line AB' at new 1 Optimal consmption bundle point (28,9) Te Scanned with CamScanner