Willy's Only Source of Wealth Is His Chocolate Factory

question 17

Multiple Choice

Willy's only source of wealth is his chocolate factory.He has the utility function pc^1/2_f + (1 - p) c^1/2_nf, where p is the probability of a flood, 1 - p is the probability of no flood, and c_f and c_nf are his wealth contingent on a flood and on no flood, respectively.The probability of a flood is p = 1/11.The value of Willy's factory is $800,000 if there is no flood and 0 if there is a flood.Willy can buy insurance where if he buys $x worth of insurance, he must pay the insurance company $4/4x whether there is a flood or not, but he gets back $x from the company if there is a flood.Willy should buy

• A)enough insurance so that if there is a flood, after he collects his insurance, his wealth will be the same whether there is a flood or not.
• B)no insurance since the cost per dollar of insurance exceeds the probability of a flood.
• C)enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/16 of what it would be if there is no flood.
• D)enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/5 of what it would be if there is no flood.
• E)enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/9 of what it would be if there is no flood.

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Definitions:

Existential Instantiation

A logical operation that infers the existence of at least one individual satisfying a particular property from a general statement.

Universal Instantiation

A logical rule of inference that allows one to deduce a particular instance from a universal statement, essentially moving from a general statement to a specific example.

Existential Generalization

A logical inference rule stating that if something is true for some member of a domain, then it is true that there exists something in that domain for which the proposition holds.

Quantifier Negation

The process of changing the quantifier in a statement, such as from "all" to "not all," to negate its original meaning.