Question

Jordan visits her sister several times a year. Jordan's travel budget is \(\$ 600,\) which she uses to buy bus tickets and train tickets. The train costs \(\$ 120\) per trip, and the bus costs \(\$ 40 .[\mathrm{LO} 7.2,7.3]\) a. Graph Jordan's budget constraint. b. How many total trips can Jordan take if she takes the train three times? c. Suppose Jordan's travel budget is cut to \(\$ 360 .\) Draw her new budget constraint. d. How many train trips can she take if she doesn't want to reduce the total number of trips she takes each year?

Short answer

a) Graph budget line 120T + 40B = 600. b) 6 bus trips. c) Graph 120T + 40B = 360. d) 2 train trips.

Step-by-step solution

Graph Jordan's Budget Constraint

Jordan spends her budget on train (T) and bus (B) trips. If the train costs \(120 per trip, then the equation for the total cost of train trips is \(120T\), and if the bus costs \)40, the cost for bus trips is \(40B\). The budget constraint is \(120T + 40B = 600\). To graph, find the intercepts: if \(T = 0\), \(B = 15\); and if \(B = 0\), \(T = 5\). Plot these on a graph as the line \(120T + 40B = 600\).

Calculate Remaining Trips

Given Jordan takes 3 train trips \(T = 3\), calculate the remaining budget for bus trips. Plug \(T = 3\) into the equation: \(120(3) + 40B = 600\). Simplify to get \(360 + 40B = 600\), and solving for \(B\) results in \(B = 6\). So, she can take 6 bus trips.

Graph New Budget Constraint

With a new budget of $360, the budget constraint changes to \(120T + 40B = 360\). Find new intercepts: if \(T = 0\), \(B = 9\); and if \(B = 0\), \(T = 3\). This line, \(120T + 40B = 360\), can be drawn to represent the new budget.

Calculate Train Trips with Constant Total Trips

The total number of trips Jordan originally takes is \(3 + 6 = 9\). With a budget of $360 and maintaining 9 total trips \(T + B = 9\), substitute \(B = 9 - T\) in the equation \(120T + 40B = 360\). This becomes \(120T + 40(9 - T) = 360\). Simplify to solve for \(T\), and you'll find \(T = 2\). So, she can take 2 train trips.

Key concepts

Microeconomics

Microeconomics explores the choices individuals and firms make regarding the allocation of resources. In our context, it concerns how Jordan allocates her travel budget on bus and train tickets. This is an example of decision-making in scarcity since Jordan's options depend upon her limited resources, which are represented by her travel budget.

• Budget Constraint: A budget constraint illustrates the combinations of goods and services that a consumer can purchase given their income and the prices of those goods and services.


• Resource Allocation: In microeconomics, every choice made by consumers, like Jordan choosing between bus and train trips, reflects an underlying trade-off due to limited resources.

Microeconomics focuses on how decisions are made, aiming to maximize satisfaction or utility while constrained by a limited budget.
By understanding Jordan's decision-making process, we get insight into consumer behavior and the principles of optimization.

Consumer Choices

Consumer choices are influenced by preferences and constraints, such as budget limitations. Jordan's decision between bus and train trips exemplifies this concept. She must decide how to allocate her $600 travel budget to maximize her satisfaction.

Preferences and Trade-offs

Consumers have preferences indicating which combinations of goods make them the happiest. Hence, Jordan might prefer train trips for comfort or time-saving. However, each train trip is more expensive, forcing her to consider budget limitations.

• Understanding preferences helps explain why one might choose fewer, more expensive train trips over numerous bus trips.


• Trade-offs between these options illustrate the choices all consumers must make when facing limited resources.

Each trip adds to her overall satisfaction, constrained by her budget, emphasizing the inherent trade-offs in consumer decision-making.

Graphical Analysis

Graphical analysis visually represents budget constraints and helps to analyze consumer choices like Jordan's. A graph can vividly demonstrate how different allocations of bus and train trips fall on or within her budget constraint.

Understanding Graphs

Graphs showcase relationships between goods and their quantities. By graphing Jordan’s budget constraint, we can visualize how many combinations of bus and train trips are possible within her budget.

• The horizontal axis might represent the number of train trips, and the vertical axis for bus trips.


• The budget constraint creates a line between two endpoints: the maximum number of train trips (at 0 bus trips) and the maximum number of bus trips (at 0 train trips).

This graphical representation facilitates understanding how changes in budget or prices alter feasible choices. For instance, a budget cut from $600 to $360 will shift the line inward, reducing the area of possible combinations, highlighting the impact of budget changes on consumer options.