91Ó°ÊÓ

Utility is a concept in economics that reflects the satisfaction or happiness a person gets from consuming goods or services. In André's case, utility is derived from playing laser tag and reading books. Each activity provides positive satisfaction, and his goal is to maximize this happiness with the money he has.

Think of utility like a personal "happiness meter". The more an individual loves an activity or item, the higher the utility. Since André enjoys both laser tag and books, he's looking to get as much enjoyment as possible within his budget of $100.

• If André loves books more, he might choose to buy more books, which increases his utility from reading.
• On the other hand, if he gets more joy from playing laser tag, then investing in more hours of that activity would raise his utility.

This balancing act between two choices reflects an individual's unique preferences and how they strive to get the greatest utility given their financial limits. André's choices depend on the utility he perceives from each additional book or hour of laser tag.

Graphing the budget line is a helpful way to visualize all possible combinations of goods that can be bought with a fixed budget. In the case of André:

• The budget equation initially is: \(10x + 20y = 100\), where \(x\) is books and \(y\) is hours of laser tag.
• By simplifying, we divide everything by 10, resulting in \(x + 2y = 10\).

The graph shows the relationship between the two goods André can buy. By plotting, we use the intercepts:

• The x-axis (horizontal) is labeled for books (\(x\)).
• The y-axis (vertical) is for hours of laser tag (\(y\)).
• We found the intercepts as \((10, 0)\) and \((0, 5)\).

These points are connected with a straight line representing the budget constraint.

André cannot purchase combinations beyond this line, as that would exceed his budget. All points on the line mean he is spending exactly $100, whereas any point inside represents underspending.

Finding intercepts is crucial when plotting a budget line. They tell us how much of each good can be bought if the entire budget is spent on only one.

**Calculating Intercepts for André:**

To find intercepts, we solve the simplified budget equation \(x + 2y = 10\).

**X-Intercept (Books)**:

• Set \(y = 0\) in \(x + 2y = 10\).
• Solving gives \(x = 10\).
• This means André can buy 10 books if he spends all \(100 on books.

**Y-Intercept (Laser Tag Hours)**:

• Set \(x = 0\) in the same equation.
• Solving yields \(y = 5\).
• This indicates he can play laser tag for 5 hours if he uses all his money there.

The intercepts \((10, 0)\) and \((0, 5)\) help in creating the graph and understanding the trade-offs André faces with his budget of \)100. Each intercept gives a boundary of his spending capacity on each of the goods.