Question

Jasmine's Snack Shop sells two brands of potato chips. She produces them by buying them from a wholesale supplier. Brand \(X\) costs Jasmine \(\$ 1\) per bag, and Brand Y costs her \$1.40. Draw Jasmine's production possibilities frontier if she has \(\$ 280\) budgeted to spend on the purchase of potato chips from the wholesaler. Why is it not "bowed out"?

Short answer

Answer: The production possibilities frontier is not "bowed out" or concave in this problem because the opportunity cost of each brand does not depend on the quantity of the other brand. The cost per bag of each brand remains constant, and when the opportunity cost is constant, the frontier will be a straight line rather than a "bowed out" shape, which indicates increasing opportunity costs.

Step-by-step solution

Find the possible combinations of potato chip bags

To find the maximum number of each brand bags she can buy, let's divide her budget by the cost of each brand: For Brand X: \(\frac{280}{1} = 280\) bags For Brand Y: \(\frac{280}{1.4} \approx 200\) bags Now we have the maximum number of bags Jasmine can buy for each brand if she only spends her budget on one type.

Set up the production possibilities frontier

To draw the production possibilities frontier, we'll use a graph where the x-axis represents the number of Brand X bags and the y-axis represents the number of Brand Y bags. We can plot the two points (280, 0) and (0, 200) as the maximum number of bags for each brand if Jasmine spends her entire budget on that brand.

Draw the production possibilities frontier

The production possibilities frontier will be a straight line connecting the two points we plotted. The equation for this line will be: \(1.4x + y = 280\) To draw the line, we can use the two points we found earlier and connect them, this represents all possible combinations of Brand X and Brand Y bags she can purchase with her budget.

Explain why the production possibilities frontier is not "bowed out."

In this case, the production possibilities frontier is not "bowed out" (concave) because the opportunity cost of each brand does not depend on the quantity of the other brand. The cost per bag of each brand remains constant at \(1 per bag for Brand X and \)1.40 per bag for Brand Y, regardless of the number of bags produced. When the opportunity cost is constant, the production possibilities frontier will be a straight line, rather than showing increasing opportunity costs with a "bowed out" shape.

Key concepts

Opportunity Cost

Understanding the concept of opportunity cost is essential when analyzing the choices made in all facets of economics, including personal budgeting and production decisions in businesses. Put simply, opportunity cost refers to the value of the next best alternative that is given up when a choice is made. In the context of Jasmine's Snack Shop, when she decides to buy a bag of Brand X potato chips, she foregoes the opportunity to spend that dollar on Brand Y chips, or anything else for that matter.

Why is this concept relevant? Well, it allows Jasmine to assess the trade-offs of her decisions. To maximize her profit or the variety of chips she offers, she should weigh the opportunity cost of different choices. Notably, the exercise shows that the opportunity cost of buying Brand Y is higher than Brand X because Brand Y eats up more of her budget per bag. This impacts how many of each brand she can afford, potentially influencing her sales strategy.

Budget Constraint

In economics, a budget constraint represents the limit on the consumption choices of individuals or firms as a result of their income or budget. It's a practical ceiling to what can be bought or invested in, and it is visually represented by the production possibilities frontier (PPF). For Jasmine's Snack Shop, her budget constraint is simple: she has \(280 to spend on potato chips.

The constraint manifests in how many bags of each brand of chips Jasmine can purchase. With a budget of \)280, Jasmine can buy up to 280 bags of Brand X (at \(1 each) or approximately 200 bags of Brand Y (at \)1.40 each), but not both in full quantity. Her budget constraint therefore forces her to make decisions about the allocation of her funds, and the combination of purchases that will best meet her objectives, whether those are to maximize variety, quantity, or some other goal.

Economic Models

Economic models are simplified versions of a more complex reality, designed to better understand the relationships between different economic variables. The PPF, the model used in Jasmine's scenario, is a prime example of such a tool. It helps in visualizing the trade-offs and constraints faced by producers.

In Jasmine's case, the model is represented by a straight line, which indicates the trade-offs and possibilities available to her given her fixed budget. Real-world complexities are set aside to focus on the fundamental relationship between the amounts of Brand X and Brand Y chips that she can buy. Economic models like the PPF are instrumental in teaching students and guiding businesses, as they make abstract concepts more tangible and provide a basis for comparison, prediction, and decision making.