Question

[Uses the Marginal Utility Approach] Anita consumes both pizza and Pepsi. The following tables show the amount of utility she obtains from different amounts of these two goods: $$\begin{array}{cc} {}{\quad\quad\quad\quad\quad}{\text {Pizza }} \\ \hline \text { Quantity } & \text { Utility } \\ \hline \text { 4 slices } & 115 \\ \text { 5 slices } & 135 \\ \text { 6 slices } & 154 \\ \text { 7 slices } & 171 \end{array}$$ $$\begin{array}{cc} \quad\quad{}{} {\text { Pepsi }} \\ \hline \text { Quantity } & \text { Utility } \\ \hline 5 \text { cans } & 63 \\ 6 \text { cans } & 75 \\ 7 \text { cans } & 86 \\ 8 \text { cans } & 96 \end{array}$$ Suppose Pepsi costs \(\$ 0.50\) per can, pizza costs \(\$ 1\) per slice, and Anita has \(\$ 9\) to spend on food and drink. What combination of pizza and Pepsi will maximize her utility?

Short answer

The exact answer may vary depending on the calculations made in steps 1-3. But the general process is to start buying the item with the highest marginal utility per dollar then switch to the other as the marginal utility per dollar falls below that of the other item due to the law of diminishing marginal utility. The process stops when the budget of $9 is exhausted.

Step-by-step solution

Determine the Marginal Utility per Dollar for Each Product

First, we need to determine the marginal utility (MU) for each product by subtracting the utility of the previous quantity from the new quantity. For example, MU of the 5th pizza slice would be \(135-115=20\) utility points. We then need to compute the MU per dollar by dividing the MU by the price of each item. In the case of the 5th pizza slice, this gives \(20/1 = 20\) utility points per dollar.

Prioritize Items with Higher Marginal Utility per Dollar

Next, we need to prioritize the product that gives a higher MU per dollar and start purchasing that until the MU per dollar falls below that of the other item. In this case, we should begin by comparing the MU per dollar of the 5th slice of pizza and the 6th can of Pepsi. The item with higher MU per dollar is selected.

Spend until the budget is exhausted

Continue buying the item that provides the higher MU per dollar until the MU per dollar falls below that of the other item. When this happens, switch to the item with the higher MU per dollar. If the budget is exhausted before this point is reached, finish purchasing at this stage. If there's still some budget left, but not enough to buy another unit of ether item, finish purchasing as well.

Key concepts

Utility Maximization

Utility maximization is the concept that consumers aim to get the most satisfaction from their available resources. In simpler terms, it's about getting the best bang for your buck.
Understanding utility maximization involves a few key aspects:

• Consumers have a limited budget to spend on various goods and services.
• They choose combinations of goods that provide the highest utility, or satisfaction, for their budget.
• The goal is not just to spend all the money, but to allocate it in a way that maximizes overall happiness.

In the case of Anita, she wants to make sure every dollar contributes as much utility as possible. This might mean buying more of a good that provides the highest utility per dollar spent. By doing this, Anita ensures that she is using her limited funds in the most efficient way possible to achieve the greatest happiness.

Consumer Choice Theory

Consumer Choice Theory explores how consumers make decisions to allocate their money across different goods and services. The theory assumes that consumers aim to maximize their overall utility, given their budget constraint.
Key elements of Consumer Choice Theory include:

• Understanding preferences: Consumers have preferences that dictate which goods they would like to buy more of.
• Budget constraint: Consumers have a limited amount of money to spend, so they can't purchase everything they want.
• Marginal utility: This measures the additional satisfaction a consumer gets from consuming an extra unit of a good.

Anita's decision involves these components. Her choices are influenced by her preferences for pizza and Pepsi and the prices of these items. By gaging how much satisfaction (utility) each additional slice of pizza or can of Pepsi provides, Anita can determine the best way to allocate her budget.

Marginal Utility per Dollar

Marginal Utility per Dollar is a measure used by consumers to ensure they are making the best possible decisions with their money. It shows how much additional utility (satisfaction) a consumer receives for each dollar spent on a good.
Key points about Marginal Utility per Dollar:

• It is calculated by dividing the marginal utility (MU) of a product by its price.
• The product with the highest MU per dollar should be purchased first to maximize satisfaction.
• As more of a product is consumed, its marginal utility tends to decrease, which is known as the law of diminishing marginal utility.

In the example involving Anita, this concept is crucial. By calculating the MU per dollar for each slice of pizza and can of Pepsi, she can determine which product will give her the most satisfaction for each dollar spent. This helps her decide which combination of purchases will maximize her total utility given her budget constraint.