Economics 101300
Winter, 2006
Homework Problem Set # 6
Problems:
1)
You decide that calculating your potential winnings from playing the lottery is
entirely too complicated and opt for a simpler way to make cash fast.
Like always, a
student group on campus, “students for (insert your favorite cause here)” is having a
raffle. Tickets are $10 and the prize is $100 in cash.
The following five percentages
represent probabilities of winning the raffle.
What is the lowest probability at which
you are willing to buy a raffle ticket?
a)
10.1%
b)
9.1%
c)
91.1%
d)
100%
e)
10%
Answer: e.
If the expected value of playing the raffle is more than 0, you are willing to
buy a ticket.
To determine the minimum probability of winning for which your EV will
be $0, solve the following equation (let x equal the probability of winning):
0= (x)(expected winnings) + (1x)(expected losses)
0 =
x(10010) + (1x)(010)
0 = 90x + 10x  10
x
= 0.1or 10%
Thus, for any percentage probability greater than 10%, it is
worth it to you to buy a raffle ticket.
2)
You are a financial consultant for Yahoo—and you have quite a bit of saving. You
know that you need to diversify your portfolio, so you invest in three financial
instruments with the expected returns listed in the following table.
What is the
expected
rate of return
on your diversified portfolio?
Bonds
Stocks
Gold
Amount Invested
$1,000
$5,000
$10,000
Expected Rate of
Return
10%
50%
25%
Answer: The expected rate of return on the diversified portfolio is the weighted average
of the returns of each asset by its dollar amount:
Expected Rate of Return = [(1,000*.10) + (5,000*.50) + (10,000*.25)]/16,000
= (100 + 2,500 + 2,500)/16,000
= 5100/16,000
= .319(or 31.9%)
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View Full DocumentNotice that this is the expected RATE of return.
In total, the expected value is $1,100 +
$7,500 + 12,500 = $21,100.
Your initial investment is $16,000.
To get the rate, you can
also calculate the total expected value and divide by the initial investment.
$21,100/$16,000 = 1.31875.
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 Winter '08
 Gerson
 Economics, Microeconomics, Supply And Demand, Debt, Probability theory, DaEng

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