Recall Bob and Ray in Problem 4

question 16

Multiple Choice

Recall Bob and Ray in Problem 4. They are thinking of buying a sofa. Bob's utility function is U_B(S, M_B) = (1 + S) M_B and Ray's utility function is U_R(S, M_R) = (4 + S) M_R, where S = 0 if they don't get the sofa and S = 1 if they do and where M_B and M_R are the amounts of money they have respectively to spend on their private consumptions. Bob has a total of $800 to spend on the sofa and other stuff. Ray has a total of $4,000 to spend on the sofa and other stuff. The maximum amount that they could pay for the sofa and still arrange to both be better off than without it is

• A) $1,000.
• B) $1,200.
• C) $1,800.
• D) $650.
• E) $2,400.

---

Definitions:

Repeated Multiplication

The process of multiplying a number by itself a specified number of times.

Simplest Form

An expression or fraction reduced to its most basic form, such that no further simplification is possible.

Exponential Form

A mathematical expression where a number is written as the base raised to a specific power or exponent, representing repeated multiplication.

Exponential Form

A way of representing numbers, typically involving expressions using powers of a base number, especially in the context of exponential growth or decay.