Question
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
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?
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