Figure 27-3

Question

The following figure shows a utility function for Dexter.

A graph of Utility versus Wealth shows a curved line that increases at an increasing rate from left to right from the origin. Values A, B, and C are marked on the vertical axis, from lowest to highest. Values $800, $1300, and $1800 are marked on the horizontal axis, from smallest to largest. The following lines extend to the curved line, from left to right. A horizontal line that extends from A and a vertical line that extends from $800. A horizontal line that extends from B and a vertical line that extends from $1300. A horizontal line that extends from C and a vertical line that extends from $1800.

Refer to Figure 27-3 . From the appearance of the graph, we know that
a. Dexter's level of satisfaction increases by less when his wealth increases from $1,001 to $1,002 than it does when his wealth increases from $1,000 to $1,001.
b. Dexter's level of satisfaction increases by the same amount when his wealth increases from $1,001 to $1,002 as it does when his wealth increases from $1,000 to $1,001.
c. Dexter's level of satisfaction increases by more when his wealth increases from $1,001 to $1,002 than it does when his wealth increases from $1,000 to $1,001.
d. the change in Dexter's level of satisfaction is constant as wealth increases.

Answer 1

Based on your description of the utility function for Dexter, we can analyze the options provided:

• The graph is characterized as a curved line that increases at an increasing rate, meaning that as wealth increases, the additional satisfaction (or utility) gained from each additional dollar decreases. This is a classic representation of diminishing marginal utility.

Given this information, we can evaluate the options:

a. Dexter's level of satisfaction increases by less when his wealth increases from $1,001 to $1,002 than it does when his wealth increases from $1,000 to $1,001.
This is accurate according to the graph's description. As the curve represents diminishing marginal utility, the increase in utility from $1,001 to $1,002 would indeed be smaller than the increase from $1,000 to $1,001.

b. Dexter's level of satisfaction increases by the same amount when his wealth increases from $1,001 to $1,002 as it does when his wealth increases from $1,000 to $1,001.
This is incorrect since the graph indicates diminishing returns to utility as wealth increases.

c. Dexter's level of satisfaction increases by more when his wealth increases from $1,001 to $1,002 than it does when his wealth increases from $1,000 to $1,001.
This contradicts the information from the graph and is therefore incorrect.

d. The change in Dexter's level of satisfaction is constant as wealth increases.
This is also incorrect, as the graph shows that the change in satisfaction (utility) is not constant but diminishes as wealth increases.

Thus, the correct answer is a. Dexter's level of satisfaction increases by less when his wealth increases from $1,001 to $1,002 than it does when his wealth increases from $1,000 to $1,001.