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Unformatted text preview: Problem 6.3 (a) The slope of the IC =_MRS r MRS = — Mal : _ A ‘3'“
MU2 0071 xx OX2 since 22x"! £131
and :1
ox:
'4; then M’RS : —2x 7" The slope of the budget line = 7 &
P2
The tangency condition is:
_ Zx‘L _ _ &
P2
\2
:> \1 : 4i ‘03 J
\ P1
(b)
Budget line condition: placl + p23:2 : m
x \ 3
Tangency condition: x1 = 4 ij
\ p1
r 2 '
:‘ 4 p—2j+pgxq 2;”
K P1
\
m a
“Esp—J
P2 \ P1 (c) If pl :1 and p2 = 2 and m :9 Then
x \2
x124] :16
\l
9 2‘ 7
2 \14 2 but we are constrained to nonnegative choices: x2 0 Since we have quasilinear utility here, the demand for no is not related to
income. Ambrose demands xi = 16 at the current prices Thus, in order for him to start demanding an, he needs to have an income
of at least 16 (sincepl = 1). Problem 6.5 If two 802 can are always as good as one 1602 can, then the goods are perfect
substitutes. The indifference curves will be straight lines with a slope of 2. Now if m = 30, p8 = 0.75 and p16 =1 , then the slope of the budget line is: _ ﬁ _ _3
ps 3
B—ounce cans
40
30
20
IO
0 IO 20 30 40 I 6—ounce cans (a) At these prices, she will only buy 16 02 cans. She can buy thirty 1602 cans or
fortyfive 8 02 cans. She prefers thirty 1602 cans. (b) If p3 lr to 0.55. she will still not buy any 802 cans. (c) If p3 Jr to 0.40. she will only buy 802 cans. She will buy seventyfive 802
cans. This gives her higher utility than the thirty 1602 cans. (d) If p16 :1 and Shirley buys some of each. it must be the case that the budget line lies across an indifference curve. This means that p8 = 0.50 (e) Demand functions: If p16 > 2103 then x16 :0 and x3 =ﬂ
PS
, m
It p16 <; 2398 then x16 : and x8 :0
P16 If p16 : 2103 then Shirley is indifferent between affordable
combinations Problem 8.3 X 30 3543 F5 90 120 (a) In the graph, log is currently at point E. (The relevant budget line
joins (0, 30) to (75, 0).) Therefore, consumption is X : 30 (b) If px Jr to $2.50. the relevant budget line joins (O, 30) to (120, 0). The new consumption point is C. Here Zog consume X : 35. (c) The income that allows Zog to have his preprice change utility at the
new prices is 225. Therefore. to afford his old indifference curve, can take up to $75 from him. (d) The total effect of the price change is represented by the change from
point E to point C.
(e) The income effect corresponds to the movement from point F to point
C. The substitution effect corresponds to the movement from point E
to point F.
(t) Since consumption of X falls (from 43 to 35) when income goes up, X is an inferior good. income 300 225 30 43 Price 30 35 Problem 8.5 If the two goods are perfect complements then the consumer has Lshaped
indifference curves. Initially The consumer has an optimal consumption bundle at A. Now suppose that the price of good X increases. The overall change is
represented as follows: Now the optimal bundle is found at point C.
Let’s decompose this change into substitution and income effects. The substitution effect holds purchasing power constant but changes the prices.
That is, in the graph below, the new budget line goes through the point A. 011 this
new budget line the optimal bundle is found at point A again. That is, there is no substitution effect. This means the entire change fromA to C is a pure income effect. ...
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 Spring '08
 Yu
 relevant budget line

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