课程名称︰个体经济学一
课程性质︰必修
课程教师︰黄贞颖
开课学院：社会科学院
开课系所︰经济学系
考试日期（年月日）︰2017/11/06
考试时限（分钟）：180
试题 :
1. Pete is a five-year-old. His mom, Melody, is a sweets lover and feeds
Pete with chocolates and ice cream. Denote (c,i) a bundle which has
c pieces of chocolates and i boxes of ice cream. Since Melody only
gives Pete finite choices, following what we leared from "GARP for
Kids: On the Development of Rational Choice Behavior," in American
Economic Review 2001, we say Pete directly reveals he prefers bundle
x' to bundle x when he chooses x' over x or over a bundle z which has
at least as much of every good as in x, and has more than x in at
least one good. We say Pete indirectly reveals that he prefers bundle
x' to bundle x when some sequence of directly preferred relations
between bundles connect x' to x.
(a) (8%) Explain, by giving an example why we need to use this
different definition of directly revealed preference. You may
need to use Figure 1 taken from the paper.
https://i.imgur.com/0WDytuY.png
(b) (8%) On Monday, Melody gave Pete choices between (5,1) and (3,3),
Pete went for (5,1). On Tuesday, Pete chose (2,4) over (6,1). On
Wendnesday, Pete went for (3,3) instead of (2,5). Does Pete
directly reveal that he prefers (3,3) to (2,4)? Explain.
(c) (8%) Continue from (b) above. Do Pete's choices satisfy the weak
axiom of revealed preference? Explain what WARP is first and then
your answer.
(d) (8%) Continue from (b) above. Do Pete's choices satisfy the
strong axiom of revealed preference? Explain what SARP is first
and then your answer.
(e) (8%) Continue from (b) above but assume instead on Monday, Pete
went for (3,3). Pete's choice on Tuesday and Wednesday remain the
same. Can you rationalize Pete's choices with a specific
preference? Explain.
2. Mars is a very wise monkey. It knows that to survive, it first has to
get enough calories from foods to meet basic needs. When that is
satisfied, it goes after the taste foods can provide as a gourment.
Fang-Chen is the master of Mars. She feeds Mars monkey chows and
grapes. They are measured in continuous amount. Monkey chows are
particularly rich in calories. Grapes are low in calories. In
particular, every monkey chow provides 4 units of calories. Every
grape provides 1 unit of calorie. Denote a consumption bundle by
(c,g) where c is the amount of monkey chows and g is the amount of
grapes in the bundle. Hence the total calories of the bundle is
4c+g. Monkey chows and grapes are both tasty, the total taste of a
bundle (c,g) is given by cg.
Mars needs at least 100 units of calories as the basic needs. Its
preference is as follows. For any two bundles, if the total calories
a bundle is at least 100 and that of the second bundle is strictly
less than 100, it prefers the former to the latter. If the total
calories of both bundles are strictly less than 100, it prefers the
one giving higher calories (and is indifferent if both bundles give
equal calories). If the total calories of both bundles are at least
100, it prefers the one with better taste (and is indifferent if both
bundles are equally tasty).
Fang-Chen loves Mars so much that whenever she goes to the local
market, she maximizes Mars' preference given her budget constraint.
If you will draw in your answers, label monkey chow on the X-axis,
grapes on the Y-axis.
(a) (10%) Fang-Chen goes to the market and finds that both the price
of monkey chows and that of grapes are 1. With m dollars at hand,
if Fang-Chen temporarily ignores the basic needs of 100 units of
calories and just considers maximizing the total taste, what
bundle Fang-Chen will choose for Mars?
(b) (10%) Continue from (a) above. Of course, in reality, Fang-Chen
cannot ignore the basic needs of 100 units of calories. Calculate
the total calories of the bundle in your answer to (a). Determine
a bound of money say m' such that when m is lower than this
bound, the total calories are less than 100 and hence Fang-Chen
needs to adjust her choice. On the other hand, when m is higher
than this bound, the total calories are more than 100 and hence
it is OK that Fang-Chen ignores the basic needs of 100 units of
calories.
(c) (10%) Continue from (b) above. Let us now figure out what
Fang-Chen should do when m is lower than m'. For that, we first
look at the case where m is lower than 25. Derive the optimal
choice in this case. Explain briefly. Are monkey chows normal or
inferior in this case?
(d) (10%) Continue from (c). Let us look at the second case where m
is higher than 25 but still lower than m'. First find the bundle
on the budget line which gives exactly 100 units of calories.
Explain in details why this bundle is the optimal choice. Are
monkey chows normal or inferior in this case?
(e) (10%) Take what you have leared so far, can you find a price of
monkey chows which is higher than 1 so that when the price of
monkey chows increases from 1 to this higher price (holding the
price of grapes fixed at 1), the demand of monkey chows
increase? Explain in details how you get your answer.
(f) (10%) We learn that the utility function is a nice convenient
way to represent preferences but it is not unique. Can you write
down a utility function of Mars? Or do you think Mars'
preference cannot be represented by any utility function?
Explain. (Hint: You need to pay particular attention to the
fact that for any two bundles, if the total calories of a bundle
is at least 100 and that of the second bundle is strictly less
than 100, Mars prefers the former to the latter.)