Question

The Smiths are a low-income family with \(\$ 10,000\) available annually to spend on food and shelter. Food costs \(\$ 2\) per unit, and shelter costs \(\$ 1\) per square foot per year. The Smiths are currently dividing the \(\$ 10,000\) equally between food and shelter. Use either the Marginal Utility Approach or Indifference Curve Approach. a. Draw their budget constraint on a diagram with food on the vertical axis and shelter on the horizontal axis. Label their current consumption choice. How much do they spend on food? On shelter? b. Suppose the price of shelter rises to \(\$ 2\) per square foot. Draw the new budget line. Can the Smiths continue to consume the same amounts of food and shelter as previously? c. In response to the increased price of shelter, the government makes available a special income supplement. The Smiths receive a cash grant of \(\$ 5,000\) that must be spent on food and shelter. Draw their new budget line and compare it to the line you derived in part \(a\). Could the Smiths consume the same combination of food and shelter as in part \(a\) ? d. With the cash grant and with shelter priced at \(\$ 2\) per square foot, will the family consume the same combination as in part \(a\) ? Why or why not?

Short answer

The Smiths currently spend $5000 on Food and $5000 on Shelter. If the price of shelter rises, they will be unable to maintain the same level of consumption. Provided with a $5000 grant, they could keep their old consumption, but they might choose different amounts depending on their preferences.

Step-by-step solution

Calculate current spending

We start by calculating the current spending of the Smiths on food and shelter, respectively. Since we know that the total budget is \$10,000 and this is divided equally, they are spending \$5,000 on food and \$5,000 on shelter. So they are buying 2500 units of food and 5000 square feet of shelter annually.

Initial budget constraint graphical representation

We then draw a budget line or constraint with food on the vertical axis and shelter on the horizontal axis. The current consumption choice would fall on the line, at 2500 units of food and 5000 square feet of shelter.

Impact of price rise in shelter

The price of a shelter rises to \$2, their budget line will rotate inward around the food axis. Now, they cannot afford to consume the same amounts of food and shelter as before with only \$10,000. They would have to consume less shelter.

Impact of income supplement

When the government supplements their income by \$5000, their total income becomes \$15,000. This shifts the budget line outward, meaning they can consume more of both goods. They could consume the same combination as in part a, but now they also have the option of more combinations.

Final situation analysis

With the cash grant and increased shelter price, the family has more money but also higher expenses. They could afford to consume the same as in part a, but they might not choose to do so. Their actual choice would depend on their preferences, as indicated by their indifference curves.