Question

Problem 5 Sam has preferences over green eggs, g, and ham, h, that can be described by u(g, h) = 3g2/3 + h. The price of green eggs is Pg and the price of ham is Ph, and Sam has Y dollars to spend. (a) Solve for Sam's demand functions for both green eggs and ham. (b) Give an (numerical) example of prices and income (Pg, Pn, Y) such that Sam's optimal bundle is an interior solution. (c) Give an (numerical) example of prices and income (Pg, Ph, Y) such that Sam's optimal bundle is a corner solution. (d) Draw two sketches, one depicting the situation in part (b) and the other the situation in (c). (e) Consider starting from your answer to part (c), and assume the price of green eggs rises. At what price pg will Sam begin to consume a positive amount of ham?

Answer 1

ith ; Pgi price of green eggs. . In iprice of ham od ş i yiichcome At optimali a) Budget constraint: hen + gpg = 7 T h en + (2 Pg=y hoor optimal bundle is given by 0 43 otherwise ; fheo ; go my otherwise sameination Corner solution

. . for interior solution let Pg=Pn=1 4 Y=9 3 ha to - 149,* = ? c011) [h=1 ] [0-60] ir lorner solution let Pg= Pn=1 4 %=7 So, h=80, ģ= }z= I=7 d) graphing part (62 Budget constraint ; 19 Py + h P j = 9 ] ka Igth=9] optimal solution glo ab=1 h (ham) a / AB Budget line 7 le optimal bundle) S E (3,1) 8,1) green eggs (y)

graphing part () Budget constraint: gpgthPm=7 1 Pg tPn=7 optimal solution . h o g = 7 hamihla He budget line 77H F optimal bundle g (green egge)