Consider the utility functions defined by U(x)=x1 ·x2 . O(x)=logx1+logx2 . and O(x)=

step 1 For this problem, we're going to graph using a graphing calculator, y equals log of x squared, a

Consider the utility functions defined by U(x)=x1 ·x2 ....

Consider the utility functions defined by
$$
\begin{aligned}
& U(x)=x_1 \cdot x_2 . \\
& O(x)=\log x_1+\log x_2 .
\end{aligned}
$$
and
$$
O(x)=\left(x_1\right)^2 \cdot\left(x_2\right)^2 .
$$

Do they imply different consumer preference orderings? Demonstrate.

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Key Concepts

Consumer Preference Ordering

Consumer preference ordering refers to the ranking of different bundles based on their utility. Utility functions that are monotonic transformations of each other yield identical preference orderings, meaning that although the numerical representations differ, the relative desirability of any two bundles remains unchanged.

Utility Functions

Utility functions assign numerical values to different bundles of goods to represent a consumer's preferences. They do not themselves describe the consumer's behavior but are used to rank bundles according to how well they satisfy the consumer's desires.

Monotonic Transformations

A monotonic transformation is a function that preserves the order of the original utility values. This means that if one bundle is preferred over another according to one utility function, any strictly increasing transformation of that function will preserve this preference ordering. Common transformations include logarithms or raising the utility to a positive power.

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