1.Makani is currently spending all of his income on bananas

and pretzels. In each of the following cases, Makani's

current consumption basket is listed as (xB; xP). The

marginal utility at this basket for each good is listed as

MUBand MUPand the price of each basket is listed as

pBand pP. In each case, determine if Makani is maxi-

mizing his utility, and if not, how he should reallocate his

spending in order to increase his utility. Makani's utility

function has diminishing marginal rate of substitution.

(a) xB= 3, xP= 9, MUB= 12, MUP= 8, pB= 14,

pP= 19

(b) xB= 8, xP= 19, MUB= 6, MUP= 18, pB= 4,

pP= 12

(c) xB= 17, xP= 13, MUB= 10, MUP= 16, pB= 5,

pP= 8

(d) xB= 4, xP= 9, MUB= 8, MUP= 19, pB= 14,

pP= 18

2.Draw a plot for each of the following situations (a-f) with

good x on the x-axis and good y on the y-axis. Make sure

to draw at least 3 indi_erence curves and a budget line.

a) A situation where the tangency condition is never sat-

is_ed.

b) A situation where the tangency condition is always

satis_ed.

c) A situation with a basket on the budget line that has

positive amounts of both goods that satis_es the tan-

gency condition, but is not optimal.

d) A situation with an optimal basket that satis_es the

tangency condition but is also a corner solution.

e) A situation where that tangency condition is satis_ed

on the budget line, but with a negative amount of

good x.

3.For each of the following situations, _nd the utility max-

imizing basket.

(a) I = 120, px= 4, py= 1, u (x; y) = 3x1=2y3=4

(b) I = 54, px= 9, py= 2, u (x; y) = 7x + 4y

(c) I = 18, px= 1, py= 3, u (x; y) = 4x1=2+ 2y

(d) I = 20, px= 2, py= 4, u (x; y) = 3x2+ 8y2

(e) I = 36, px= 4, py= 6, u (x; y) = 2xy 28x

4.Tom is trying to decide whether or not to join the dis-

count grocery store. He consumes food (good x) and a

composite good (good y with py= 1). He currently has

an income of I = 80 and faces a price of px= 3 if he

doesn't join the discount grocery store. If he pays the fee

F = 34 and joins the discount grocery store, then he will

only have to pay px= 1 for food. He faces the utility

function u (x; y) = 6x1=2+ y.

(a) Draw a graph of his set of available baskets if he

doesn't join the discount grocery store.

(b) On the same plot, draw a graph of his set of available

baskets if he does join the discount grocery store.

(c) Determine his optimal basket if he doesn't join.

(d) Determine his optimal basket if he does join.

(e) Should he join the discount grocery?