[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?

Step by step solution

01

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.

02

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.

03

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.

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