Rejection of the Negative Root in the Utility Equivalence Simplification

Equivalence of a $1,560 Unearned Income and a Wage Rise to $150 in Utility Terms (Figure E3.4)

In an economic model, two scenarios are found to provide equal utility to an individual when the equation 32X^2 = 50Y^2 is satisfied. Here, X and Y represent consumption levels, which must be non-negative. To make this relationship easier to work with, it should be simplified to its most basic linear form. What is the correct simplified equation?

Simplifying an Economic Relationship

In an economic model comparing two investment strategies, the point of equal value is described by the equation 48X^2 = 75Y^2, where X and Y represent positive investment amounts. To make the relationship easier to analyze, this equation is simplified to its most basic linear form. Complete the simplified equation: 4X = ___.

In an economic model comparing two choices, the point of indifference is represented by the equation 64X^2 = 100Y^2, where X and Y are positive values. A student simplifies this equation to the linear form 32X = 50Y. This simplification is a valid and correct step for making the equation easier to work with.

Analyzing a Flawed Economic Calculation

In various economic models, a state of equal value or utility between two positive quantities, X and Y, is often represented by a quadratic equation. To facilitate further analysis, these equations are simplified to a linear form. Match each quadratic equation to its correct simplified linear form.

Justifying a Mathematical Simplification in Economic Modeling

An economic model establishes that two choices provide equal value when 96X^2 = 150Y^2, where X and Y are positive quantities. To use this relationship in further calculations, it must be simplified to a linear form. Arrange the following steps into the correct logical sequence to perform this simplification.

Critiquing an Economic Analysis

Evaluating Simplification Strategies