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Chapter 4: Problem 6

Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consume and from the amount of goods \((G)\) they consume. In order to maximize utility, they need to allocate the 24 hours in the day between leisure hours and work hours. Assume that all hours not spent working are leisure hours. The price of a good is equal to \(\$ 1\) and the price of leisure is equal to the hourly wage. We observe the following information about the choices that the two individuals make: $$\begin{array}{|cccccc|} \hline & & \text { SAM } & \text { BARB } & \text { SAM } & \text { BARB } \\ \hline \begin{array}{c} \text { PRICE } \\ \text { OF 6 } \end{array} & \begin{array}{c} \text { PRICE } \\ \text { OF L } \end{array} & \begin{array}{c} \mathbf{L} \\ \text { (HOURS) } \end{array} & \begin{array}{c} \mathbf{l} \\ \text { (HOURS) } \end{array} & \mathbf{G}(\mathrm{S}) & \mathbf{G}(\mathrm{S}) \\ \hline 1 & 8 & 16 & 14 & 64 & 80 \\ \hline 1 & 9 & 15 & 14 & 81 & 90 \\ \hline 1 & 10 & 14 & 15 & 100 & 90 \\ \hline 1 & 11 & 14 & 16 & 110 & 88 \\ \hline \end{array}$$ Graphically illustrate Sam's leisure demand curve and Barb's leisure demand curve. Place price on the vertical axis and leisure on the horizontal axis. Given that they both maximize utility, how can you explain the difference in their leisure demand curves?

Short Answer

Expert verified
The leisure demand curves of Sam and Barb are the graphical illustrations of how the quantity demanded for leisure changes with changes in the wage rates. The difference in their leisure demand curves might be due to their personal preferences for leisure. For example, if Barb's demand curve is steeper, she likely values leisure time more than Sam and is less responsive to wage rate changes.

Step by step solution

01

Gather Data for Sam

Extract Sam's leisure hours and the price of leisure from the given dataset. The hourly wage is the price of leisure and quantity of leisure is simply Leisure (Hours) for Sam.
02

Plot Sam's Leisure Demand Curve

Using the data from Step 1, plot the leisure demand curve by placing the price of leisure on the vertical axis and leisure hours on the horizontal axis. The demand curve should be downward sloping, as the higher the price of leisure (higher wages), the less leisure time Sam will demand (work more).
03

Gather Data for Barb

Similarly, extract Barb's leisure hours and the price of leisure from the dataset. The quantity of leisure is the Leisure (Hours) for Barb.
04

Plot Barb's Leisure Demand Curve

Plot the leisure demand curve for Barb, analogous to Step 2. The leisure demand curve would likely be different from Sam's, reflecting her personal preferences.
05

Compare and Explain difference

Compare the leisure demand curves between Sam and Barb. Their curves might be different due to differences in preferences for goods and leisure. For instance, if Barb's curve is steeper than Sam's, it implies she is less responsive to changes in the wage rate in terms of her demand for leisure (i.e., Barb may value leisure time more than Sam).

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Most popular questions from this chapter

By observing an individual's behavior in the situations outlined below, determine the relevant income elasticities of demand for each good (i.e., whether it is normal or inferior). If you cannot determine the income elasticity, what additional information do you need? a. Bill spends all his income on books and coffee. He finds \(\$ 20\) while rummaging through a used paperback bin at the bookstore. He immediately buys a new hardcover book of poetry. b. Bill loses \(\$ 10\) he was going to use to buy a double espresso. He decides to sell his new book at a discount to a friend and use the money to buy coffee. c. Being bohemian becomes the latest teen fad. As a result, coffee and book prices rise by 25 percent. Bill lowers his consumption of both goods by the same percentage. d. Bill drops out of art school and gets an M.B.A. instead. He stops reading books and drinking coffee. Now he reads the Wall Street Journal and drinks bottled mineral water.

An individual sets aside a certain amount of his income per month to spend on his two hobbies, collecting wine and collecting books. Given the information below, illustrate both the price-consumption curve associated with changes in the price of wine and the demand curve for wine. $$\begin{array}{|ccccc|} \hline \begin{array}{c} \text { PRICE } \\ \text { WINE } \end{array} & \begin{array}{c} \text { PRICE } \\ \text { B00K } \end{array} & \begin{array}{c} \text { QUANTITY } \\ \text { WINE } \end{array} & \begin{array}{c} \text { QUANTITY } \\ \text { BOOK } \end{array} & \text { BUDGET } \\ \hline \$ 10 & \$ 10 & 7 & 8 & \$ 150 \\ \hline \$ 12 & \$ 10 & 5 & 9 & \$ 150 \\ \hline \$ 15 & \$ 10 & 4 & 9 & \$ 150 \\ \hline \$ 20 & \$ 10 & 2 & 11 & \$ 150 \\ \hline \end{array}$$

Suppose the income elasticity of demand for food is 0.5 and the price elasticity of demand is \(-1.0 .\) Suppose also that Felicia spends \(\$ 10,000\) a year on food, the price of food is \(\$ 2,\) and that her income is \(\$ 25,000\) a. If a sales tax on food caused the price of food to increase to \(\$ 2.50,\) what would happen to her consumption of food? (Hint: Because a large price change is involved, you should assume that the price elasticity measures an arc elasticity, rather than a point elasticity.) b. Suppose that Felicia gets a tax rebate of \(\$ 2500\) to ease the effect of the sales tax. What would her consumption of food be now? c. Ts she better or worse off when given a rebate equal to the sales tax payments? Draw a graph and explain.

The ACME Corporation determines that at current prices, the demand for its computer chips has a price elasticity of -2 in the short run, while the price elasticity for its disk drives is -1 a. If the corporation decides to raise the price of both products by 10 percent, what will happen to its sales? To its sales revenue? b. Can you tell from the available information which product will generate the most revenue? If yes, why? If not, what additional information do you need?

The director of a theater company in a small college town is considering changing the way he prices tickets. He has hired an economic consulting firm to estimate the demand for tickets. The firm has classified people who go to the theater into two groups and has come up with two demand functions. The demand curves for the general public \(\left(Q_{x p}\right)\) and students \((Q)\) are given below: \\[ \begin{array}{l} Q_{g p}=500-5 P \\ Q_{s}=200-4 P \end{array} \\] a. Graph the two demand curves on one graph, with \(P\) on the vertical axis and \(Q\) on the horizontal axis. If the current price of tickets is \(\$ 35,\) identify the quantity demanded by each group. b. Find the price elasticity of demand for each group at the current price and quantity. c. Is the director maximizing the revenue he collects from ticket sales by charging \(\$ 35\) for each ticket? Explain. d. What price should he charge each group if he wants to maximize revenue collected from ticket sales?
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