York University
ASSIGNMENT I
Course Director: S.H. Chiang
Course Number: ECON 2300.03A
I Figure out the budget constraint functions for the following cases:
a. An individual receives $100 from the Government.
b. Assume that  =  = 1. A subsidy is given in terms of coupons. This
allows you to get 10 units of X free of charge.
c. Suppose the recepient is able to sell his coupons at $05. What happens
to your answer in (b)?
d. Rationing (0 ) is imposed on your consumption of X.
e. Pizza Pizza has sales promotion lately. If you buy a pizza of any size at
the regular price, you can get the second one for a half price.
f. Sales taxes are imposed on X.
g. Sales taxes are imposed on X and Y.
II. Consider the utility functions:
a.  =  + ;
b.  = min[2 ];
c.  =  + ;
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d.  =  + ;
e. Lexicographic preference;
f.  =    .
What is the effect of income on  and ? Are they normal, inferior, or neutral?
III. Engineering students face the following money prices for lab notebooks (N) and
computer diskettes (D) at the Bookstore: $500 per N and for D, $1000 for the
first 10 and a 10 discount for each ten thereafter. Thus, the cost is $19 for 20
diskettes, $271 for 30, etc. Draw up the budget line of a student with $20000
to spend. What is the price of a lab book in terms of diskettes? (HINT: make
a list for  = 1 2 3 .)
IV. Suppose that, in order to eat pretzels and drink beer, you need both time and
money. Indeed, let the money price of a bag of pretzels be  = $50 and the
money price of a bottle of beer be  = $100, and suppose you have $500 to
spend. But you have only two hours in which to spend it, and it takes you 1/2
hour to eat a bag of pretzels and 15 minutes to down a brew.
(a) Draw the two budget lines and tell me their slopes.
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(b) Suppose that you can buy and sell time for $200 an hour. That is, you
can take some of your two hours and wash dishes, so that you have more
cash to spend during the remaining time, or you can pay someone to take
your washing job, and have more time to spend less cash. Draw up a new
budget line in which you have combined your money and time resources,
where you start from $500 and add what you earn or deduct what you
spend, and in which time costs have a money value.
V. Consider a person who has the following preference-ordering system for two
goods, X and Y, which exhaust his consumption space.
i. Given any two bundles (  ) he always prefers the bundle with more
X.
ii Given two bundles with the same amount of X, he prefers the one with
more Y.
Answer:
(a) Are the person’s preferences compatible with ”rational behaviour”? Why?
(b) Would the behaviour of this person as a consumer be in accordance with
the basic ”laws of demand” you have learned so far?
(c) Could you predict the exact values of this person’s income and price elasticities of demand for X and Y? (In your answer, discuss both the compensated and uncompensated price elasticities.)
VI. Bernice has the utility function ( ) = [ ]. The price of x used to be
3, but rose to 4. The price of y remained constant at 1. Her income is 12. The
price increase was as bad for her as a loss of 3 dollars in income, but she would
need an income of 16 dollars to be able to afford a bundle as good as her old
one at the new price. True or false? Why?
VII. Suppose that stock A has an equal chance of going up 20 percent and going
down 10 percent. Stock B has an equal chance of going up 30 percent and going
down 20 percent during the same period. What is the expected return for the
two stocks? Which one will a risk-averse (risk-loving) individual prefer?
VIII. Show that the utility function  =  + ( ) gives the same demand functions
as  =  .
IX. Suppose there is a 50-50 chance that a risk-averse individual with a current
wealth of $20 000 will contract a debilitating condition and suffer a loss of
$10 000.
(a) Calculate the cost of actuarially fair insurance in this situation and use a
utility of wealth graph to show that the individual will prefer fair insurance
against this loss to accepting the gamble uninsured.
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(b) Suppose two types of insurance policies are available: (i) A fair policy
covering the complete loss and (ii) A fair policy covering only half of any
loss incurred. Calculate the cost of the second type of policy and show
that the individual will generally regard it as inferior to the first.
(c) Suppose individuals who purchase cost-sharing policies of the second type
take better care of their health, thereby reducing the loss suffered when ill
to only $7 000. In this situation what will be the cost of a cost-sharing
policy? Show that some individuals may now prefer this type of policy.
X. In Japan, golfers who get a ”hole-in-one” are expected to give gifts to relatives,
fellow workers and friends. These gifts can cost them the equivalent of thousands of dollars. The cost is so great that there actually exists a market for
”hole-in-one” insurance. This problem concerns a particular golfer and his decision about whether to buy such insurance. Yoshitsugu Kanemoto, who is an
expected utility maximizer, has the following utility function for annual income,
I (measured in millions of yen):
 = ()
His annual income is 3 million yen (equivalent to about $25 000 U.S. at the
time of writing). Yoshi figures (correctly) that he has a 1 in 1000 chance of
getting a hole-in-one in a particular year. If he gets a hole-in-one, he expects
to spend .25 million yen for gifts.
(a) Is Yoshi risk averse? [Hint: find ”() and determine its sign.]
(b) Compute Yoshi’s expected utility. [Find the answer as accurately as your
calculator permits - at least to seven decimal places. This is because his
income is measured in millions, rather than units.]
(c) Compute the maximum premium, p, that Yoshi would be willing to pay
for an insurance policy that would pay him .25 million yen if he gets a holein-one. [Hint: Find the p for which U(I-p) is just equal to the expected
utility that you found in (2). Round your answer to the nearest yen.]
(d) If the actual premium charged was actuarially fair, how much would it be?
[Hint: how much would the insurance company expect to pay Yoshi in any
given year?] Would Yoshi buy insurance at this price?
(e) In fact, the actual premium is 260 yen. Will Yoshi buy the insurance?
XI. Prove the Slutsky equation.
XII. Show that a risk-averse investor can improve his utility through diversification.
XIII. Questions at end of each chapter:
• Ch2: 1, 6, 7;
• Ch3: 7, 9, 10;
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• Ch4: 4, 5, 6;
• Ch5: 1, 3, 6;
• Ch6: 1, 2, 3;
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