Question

1/2 given by u (r1, ) Sophie's preferences over two goods per unit and good 2 costs $1 per-unit 40r 2. Good 1 costs $2 are a) Sketch Sophie's income offer curve in a clearly labelled diagram. (1 point) $250 on the two b) Find the optimal consumption bundle when Sophie is spending goods. Illustrate your answ m swer in the above diagrams. (1 point) c) Suppose that the price of good 1 increases to $4 per-unit. Under the assumption that Sophie is still spending $250 on the two goods, find the income and the substitution effects with respect to good 1. Verify that the Slutsky equation holds. (2.5 points) d) Redo part d) but now find the income and substitution effects for good 2 when the price of good 1 increases to $4. Provide the economic interpretation of your numbers. (2.5 points) e) Show that the consumer is worse-off after the price of good 1 increases to p2 = $4. (1 point)

Answer 1

ANSWER a) Given 6at Ya 4071 and Pa,a 00t Let 2/1 MPS 40. (71 MRS 20 au/ana and M-PA en d loo M-200. M-a00 Off es Cuive So phie' income Ine Cou16en ib M2-00 Md00 2 MI-00 100

when sophie too oed optmal COnjumpti on bundle spending $a50 nen, dtagram L Pom an a) above he and aod +2 M-a00 950-200 - 50 and loo 50. Suppose 1nen M 250 PI $y and wi nespet effects he income substitution good 1 to necesity food 1 because, l00 exint effect income 400) L ':. 4l0o 4oo Pasuible aro mad Constant's 62.5 NO

effect for god and subaitution inome when to y increay e Ine price and $y 1-e 5 en SE= TEEO when P a Pa- C 100 250) 450 40x 10 t5O 40 100 50 6a.5, aa= 0) 316 2 40 V6as ulcu COTsume cwOrye inurease afte Price ay