straight, with slope = 6/5
Rajan has wellbehaved preferences, and his optimal bundle contains 10 scones.
b) (4) Illustrate his optimal bundle in your diagram for (a); label it A.
Why
is this choice optimal?
What conditions does it satisfy?
Ans: Why optimal?
Max's utility on his feasible set; Two conditions:
i)
MRS=(price of bananas)/(price of scones);
ii)
ii) all income is spent  bundle is on budget line.
Picture: needs an IC tangent to BL at point corresponding to 10 scones.
c) (2) How many kg of bananas does he buy?
(Show how you derived
this number.)
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Economics 203 (F01), 2005; midterm 1
Page 3 of 5
Ans: derivation  uses budget constraint:
0.6
0.5
10
b
s
x
x
+
=
.
Substituting in for
the value of
10
s
x
=
yields
1
50/6
25/3
8
3
b
x
=
=
=
kg of bananas.
d) (3) Suppose the price of bananas doubles.
In your diagram for (a),
identify the total effect of this price increase on Rajan's optimal choice.
(Label his new optimal bundle G.)
Ans: if price of bananas doubles, BL pivots about vertical axis; new horizontal
intercept is 100/12=25/3.
New optimal bundle is on new BL, where IC is tangent to BL.
Notice: there is no need for the number of scones to be the same in bundles A
and G; in fact, it would be unusual if the number did not change.
e) (6) Briefly explain the meaning of the following terms:
i)
the substitution effect of the price change on both goods;
Ans: the substitution effect measures the change in the quantity purchased in
response to a change in
relative
prices.
The doubling of the price of bananas,
with a constant price of scones, means that bananas are now more expensive
relative to scones.
Because the individual is willing to make tradeoffs between
the two goods (the IC is negatively sloped), the increased relative price of
bananas should lead Rajan to purchase more scones, and fewer bananas.
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 Fall '12
 Danvo
 Economics, Microeconomics, optimal bundle, Rajan

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