Ben allocates his lunch budget between two goods, pizza and burritos. a. Illustrate Ben's optimal bundle on a graph with pizza on the horizontal axis. b. Suppose now that pizza is taxed, causing the price to increase by 20 percent. Illustrate Ben's new optimal bundle. c. Suppose instead that pizza is rationed at a quantity less than Ben's desired quantity. Illustrate Ben's new optimal bundle.

Imagine you have a fixed amount of money to spend on lunch. The budget constraint depicts all the combinations of pizza and burritos that you can afford with your lunch budget.

It’s a simple but powerful concept: if you spend more on pizza, you can afford fewer burritos, and vice versa. The budget constraint line slopes downward on a graph, reflecting this trade-off.

Impact of a Price Change

When the price of pizza increases, for instance due to a tax, your budget constraint shifts. It becomes steeper because now, each pizza costs more, meaning you have to give up even more burritos to get the same amount of pizza—or settle for less pizza if you don’t reduce your burrito consumption. This change can significantly affect what you can afford and will likely alter your eating habits unless you decide to increase your overall lunch budget.

Our preferences can be illustrated using indifference curves. These curves represent combinations of goods, in this case, pizza and burritos, that give you the same level of happiness or satisfaction. The further from the origin an indifference curve lies, the greater the level of satisfaction.

These curves never cross and they are generally downward sloping and convex to the origin. The shape is because we tend to prefer a variety of items over a significant quantity of one item, reflecting diminishing marginal returns.

Interacting with Budget Constraints

Let’s say you can choose any combination of pizza and burritos along your budget constraint. The optimal choice is where an indifference curve just touches the budget constraint—this is where you’re getting the most satisfaction possible from what you can afford.

The optimal bundle is the sweet spot where the budget constraint and an indifference curve touch each other. It's the point where you get the maximum satisfaction without spending more than you have.

When you choose this bundle, you're effectively balancing your preferences with your budget. It’s a rational choice that provides the most 'bang for your buck.'

Effects of Price Changes and Rationing

Any changes in the price of pizza or burritos can shift what this optimal bundle looks like. For example, a tax on pizza will shift your optimal bundle toward more burritos. If pizza is rationed, your choices are limited, and your optimal bundle will adjust according to the new constraints — often leading to less satisfaction as you cannot reach higher indifference curves you could access before rationing.

When the price of pizza increases, will you keep buying the same amount, or will you cut back? Price elasticity of demand measures your likely response to price changes, telling us how much the quantity demanded of a good responds to a change in price.

A product is said to be price elastic if a small price change leads to a significant change in the quantity demanded. In contrast, if the quantity demanded remains relatively stable despite price changes, the product is price inelastic. The elasticity depends on several factors, including the availability of substitutes, necessity, and the proportion of income spent on the good.

Applying Elasticity to Optimal Bundles

In Ben's case, if pizza has many substitutes or takes up a large part of Ben's budget, the demand for pizza might be elastic. Thus, when the price of pizza increases, Ben might significantly reduce the quantity of pizza he buys and opt for more burritos instead, leading to a new optimal bundle.