Figure 14-1. The figure shows a utility function.
-Refer to Figure 14-1. Let 0A represent the distance between the origin and point A; let AB represent the distance between point A and point B; etc. Which of the following ratios best represents the marginal utility per dollar when wealth increases from $400 to $600?
A) $$\frac { 0 \mathrm {~A} } { 600 }$$
B) $$\frac { A B } { 600 }$$
C) $$\frac { 0 B } { 200 }$$
D) $$\frac { A B } { 200 }$$

Question

Figure 14-1. The figure shows a utility function. 
-Refer to Figure 14-1. Let 0A represent the distance between the origin and point A; let AB represent the distance between point A and point B; etc. Which of the following ratios best represents the marginal utility per dollar when wealth increases from $400 to $600?
A) $$\frac { 0 \mathrm {~A} } { 600 }$$ 
B) $$\frac { A B } { 600 }$$ 
C) $$\frac { 0 B } { 200 }$$ 
D) $$\frac { A B } { 200 }$$

Quizplus · Accepted Answer

The marginal utility per dollar is given by the slope of the utility function, which is the ratio of the vertical change (change in utility) to the horizontal change (change in wealth). When wealth increases from $400 to $600, the horizontal change is $200. The vertical change can be approximated by the distance AB, which represents the change in utility when the wealth increases from $400 to $500. Therefore, the ratio that best represents the marginal utility per dollar is AB/200.

Figure 14-1 0 A600\frac { 0 \mathrm {~A} } { 600 }6000 A​

Figure 14-1 $\frac { 0 \mathrm {~A} } { 600 }$