Chapter 6: Problem 8
"If a good is inferior, a rise in its price will cause people to buy more of it, thus violating the law of demand." True or false? Explain.
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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?
When an economy is experiencing inflation, the prices of most goods and services are rising but at different rates. Imagine a simpler inflationary situation in which all prices, and all wages and incomes, are rising at the same rate, say 5 percent per year. What would happen to consumer choices in such a situation? (Hint: Think about what would happen to the budget line.)
[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?
[Uses the Indifference Curve Approach] With the quantity of popcorn on the vertical axis and the quantity of ice cream on the horizontal axis, draw indifference maps to illustrate each of the following situations. (Hint: Each will look different from the indifference maps in the appendix, because each violates one of the assumptions we made there.) a. Larry's marginal rate of substitution between ice cream and popcorn remains constant, no matter how much of each good he consumes. b. Heather loves ice cream but hates popcorn.
Suppose that 1,000 people in a market each have the same monthly demand curve for bottled water, given by the equation \(Q^{D}=100-25 P,\) where \(P\) is the price for a 12 -ounce bottle in dollars. a. How many bottles would be demanded in the entire market if the price is \(\$ 1 ?\) b. How many bottles would be demanded in the entire market if the price is \(\$ 2 ?\) c. Provide an equation for the market demand curve, showing how the market quantity demanded by all 1,000 consumers depends on the price.
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