Expected Value Exercise 2

Expected Value Exercise 2

John Smith is considering the purchase of a used car that has a bank book value of $16,000.  He believes that there is a 20% chance that the car's transmission is damaged.  If the transmission is damaged, the car would be worth only $12,000 to Smith.   

What is the expected value of the car to Smith?

Expected Value Exercise 1

Expected Value Exercise

Tom Wilson is the operations manager for BiCorp, a real estate investment firm.  Tom must decide if BiCorp is to invest in a strip mall in a northeast metropolitan area.   

If the shopping center is highly successful, after tax profits will be $100,000 per year.  Moderate success would yield an annual profit of $50,000, while the project will lose $10,000 per year if it is unsuccessful.  Past experience suggests that there is a 40% chance that the project will be highly successful, a 40% chance of moderate success, and a 20% probability that the project will be unsuccessful.

a.      Calculate the expected value and standard deviation of profit.

b.      The project requires an $800,000 investment.  If BiCorp has an 8% opportunity cost on invested funds of similar riskiness, should the project be undertaken?

Inferior Good | an individual allocates his or her entire budget between two goods, food and clothing

Suppose that an individual allocates his or her entire budget between two goods, food and clothing. Can both goods be inferior? Explain.

ANSWER

No, the goods cannot both be inferior; at least one must be a normal good. Here’s why. If an individual consumes only food and clothing, then any increase in income must be spent on either food or clothing or both (recall, we assume there are no savings and more of any good is preferred to less, even if the good is an inferior good). If food is an inferior good, then as income increases, consumption of food falls. With constant prices, the extra income not spent on food must be spent on clothing. Therefore as income increases, more is spent on clothing, i.e., clothing is a normal good.

Individual and Market Demand | Difference

Explain the difference between each of the following terms:

a.   a price consumption curve and a demand curve

b.   an individual demand curve and a market demand curve

c.   an Engel curve and a demand curve

d.   an income effect and a substitution effect

ANSWER

a.   a price consumption curve and a demand curve

The price consumption curve (PCC) shows the quantities of two goods a consumer will purchase as the price of one of the goods changes, while a demand curve shows the quantity of one good
a consumer will purchase as the price of that good changes. The graph of the PCC plots the quantity of one good on the horizontal axis and the quantity of the other good on the vertical axis. The demand curve plots the quantity of the good on the horizontal axis and its price on the vertical axis.

b.   an individual demand curve and a market demand curve

An individual demand curve plots the quantity demanded by one person at various prices. A market demand curve is the horizontal sum of all the individual demand curves. It plots the total quantity demanded by all consumers at various prices.

c.   an Engel curve and a demand curve

An Engel curve shows the quantity of one good that will be purchased by a consumer at different income levels. The quantity of the good is plotted on the horizontal axis and the consumer’s income is on the vertical axis. A demand curve is like an Engel curve except that it shows the quantity purchased at different prices instead of different income levels.

d.   an income effect and a substitution effect

Both the substitution effect and income effect occur because of a change in the price of a good. The substitution effect is the change in the quantity demanded of the good due to the price change, holding the consumer’s utility constant. The income effect is the change in the quantity demanded of the good due to the change in purchasing power brought about by the change in the good’s price.

Expected Value & Variance

Consider a lottery with three possible outcomes:

●    $125 will be received with probability 0.2

●    $100 will be received with probability 0.3

●    $50 will be received with probability 0.5 

a.   What is the expected value of the lottery?

b.   What is the variance of the outcomes?

c.   What would a risk-neutral person pay to play the lottery?

ANSWER

a.   What is the expected value of the lottery?

The expected value, EV, of the lottery is equal to the sum of the returns weighted by their probabilities:

EV = (0.2)($125) + (0.3)($100) + (0.5)($50) = $80.

b.   What is the variance of the outcomes?

The variance, s², is the sum of the squared deviations from the mean, $80, weighted by their probabilities:

s² = (0.2)(125 - 80)² + (0.3)(100 - 80)² + (0.5)(50 - 80)² = $975.

c.   What would a risk-neutral person pay to play the lottery?

A risk-neutral person would pay the expected value of the lottery: $80.