Suppose a consumer as a value function over gains given by $U(z)=z$. If $x0$ and $y0$ then which of the following is true?

Question

Suppose a consumer as a value function over gains given by $U(z)=z$. If $x>0$ and $y>0$ then which of the following is true?

Quizplus · Accepted Answer

Given the linear utility function $U(z) = z$, the consumer's valuation of gains is linear, meaning the total utility from any combination of gains is simply the sum of the individual utilities. Therefore, whether gains are integrated or segregated does not affect the total utility, making the consumer equally well off in either scenario.

Suppose a Consumer as a Value Function Over Gains Given U(z)=zU(z)=zU(z)=z

Suppose a Consumer as a Value Function Over Gains Given $U(z)=z$