7.7: Exercises for Chapter 7

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EXERCISE 7.1

Henry is contemplating opening a microbrewery and investing his savings of $100,000 in it. He will quit his current job as a quality controller at Megaweiser where he is paid an annual salary of $50,000. He plans on paying himself a salary of $40,000 at the microbrewery. He also anticipates that his beer sales minus all costs other than his salary will yield him a surplus of $55,000 per annum. The rate of return on savings is 7%.

Calculate the accounting profits envisaged by Henry.
Calculate the economic profits.
Should Henry open the microbrewery?
If all values except the return on savings remain the same, what rate of return would leave him indifferent between opening the brewery and not?

EXERCISE 7.2

You see an advertisement for life insurance for everyone 55 years of age and older. The advertisement says that no medical examination is required prior to purchasing insurance. If you are a very healthy 57-year old, do you think you will get a good deal from purchasing this insurance?

EXERCISE 7.3

In which of the following are risks being pooled, and in which would risks likely be spread by insurance companies?

Insurance against Alberta's Bow River Valley flooding.
Life insurance.
Insurance for the voice of Avril Lavigne or Celine Dion.
Insuring the voices of the lead vocalists in Metallica, Black Eyed Peas, Incubus, Evanescence, Green Day, and Jurassic Five.

EXERCISE 7.4

Your house has a one in five hundred probability chance of burning down in any given year. It is valued at $350,000.

What insurance premium would be actuarially fair for this situation?
If the owner is willing to pay a premium of $900, does she dislike risk or is she indifferent to risk?

EXERCISE 7.5

If individuals experience diminishing marginal utility from income it means that their utility function will resemble the total utility functions developed graphically in Section 6.2. Let us imagine specifically that if Y is income and U is utility, the individual gets utility from income according to the relation .

In a spreadsheet or using a calculator, calculate the amount of utility the individual gets for all income values running from $1 to $25.
Graph the result with utility on the vertical axis and income on the horizontal axis, and verify from its shape that the marginal utility of income is declining.
Using your calculations, how much utility will the individual get from $4, $9 and $16?
Suppose now that income results from a lottery and half of the time the individual gets $4 and half of the time he gets $16. How much utility will he get on average?
Now suppose he gets $10 each time with certainty. How much utility will he get from this?
Since $10 is exactly an average of $4 and $16, can you explain why $10 with certainty gives him more utility than getting $4 and $16 each half of the time?

EXERCISE 7.6

In Question 7.5, suppose that the individual gets utility according to the relation Repeat the calculations for each part of the question and see if you can understand why the answers are different.

1. A different form of risk management is defined by the idea of risk spreading. Imagine that an oil supertanker has to be insured and the owner approaches one insurer. In the event of the tanker being ship-wrecked the damage caused by the resulting oil spill would be catastrophic – both to the environment and the insurance company. In this instance the insurance company may not benefit from the law of large numbers – it may not be insuring thousands of tankers and therefore would find it difficult to balance the potential claims with the annual insurance premiums. As a consequence, an insurer will spread the potential cost among other insurers – this is called risk spreading. The world's major insurers, such as Lloyd's of London, have hundreds of syndicates who each take on a small proportion of a big risk. These syndicates may again choose to subdivide their share among others, until the big risk becomes widely spread. In this way it is possible to insure against almost any event or possibility, no matter how large.