**BUS 143: Assignment 1**

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**All the answers have to be typed. Bring them over to class. **

**This assignment is due on October 10, 2013.**

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(20) Question 1. For each of the four gambles below calculate the expected monetary outcome (expected value) and find that option (or options) which maximizes net expected payoff:

Gamble 1: Three prizes $20, $8, and $4 with respective probabilities ½, ¼, and ¼.

There is an entry fee of $3.

Gamble 2. Two prizes of $20 and $6 with equal likelihood. There is an entry fee of $4.

Gamble 3: Three prizes of $20, $6 and $1 with equal likelihood. There is no entry fee.

Gamble 4: Three prizes of $32, $20, and -$24 with respective probabilities of ½, ¼, and ¼. There is an entry fee of $5.

(25) Question 2. A merchant has possessions valued at $50,000 which are susceptible to accidental destruction (e.g., fire, flood). For a fee of *f* dollars he is guaranteed against any loss. He estimates the probability of an accident to be 0.1.

(i) If the merchant evaluates his options in terms of the expected money (value) criterion would he opt for insurance when the fee is $5,500?

(ii) If the merchant had a utility function of the form u(*x*) = *x*^{0.4}, would he opt for an insurance if he evaluated his options in terms of expected utility?

(iii) What is the maximum amount of money the merchant would pay for insurance if he used the expected utility criterion?

(25) Question 3. A firm is offered a contract to develop an electronics subsystem for a new airplane. If the system is developed within two years the profit will be $500,000. But if development takes longer, a loss of $2.5 million will be incurred. The Research and Development (R&D) department of the firm assesses the probability of development within two years to be 0.9.

(i) If the firm has a linear utility for money, ought it to take the contract or not?

(ii) If the utility of money is given by u(*x*) = 2*x *- 0.1*x*^{2 }+ 100 (where *x* is the firm’s assets in millions of dollars), what will the decision be, assuming that the current assets are $3 million?

(iii) In what way is the utility function in (ii) above unusual?

(30) Question 4. A company whose assts are $3 million must decide whether or not to enter into a research and development project whose outcome is uncertain. If the project succeeds, this will *increase* the assets by $1 million. If it fails, the firm’s assets will be *reduced* to $500,000. Find the minimal probability of project success, which would lead the company to enter into the project, given that the criterion used to evaluate the two options is one of the following:

(i) expected money outcome;

(ii) expected utility outcome with utility functions as follows, where *x* is in millions of dollars:

(a) u(*x *) = *x*^{1/2}

(b) u(*x*) = *x *- 0.1*x*^{2}

(c) u(*x*) = 1 - *e*^{-x}

(d) u(*x*) = 1 - (3/4)^{x}

Which of these four functions is consistent with risk-aversion?

Which of these functions is bounded over all non-negative values of *x*?

Subject | Business |

Due By (Pacific Time) | 10/10/2013 12:30 pm |

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