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Chapter 6: Problem 14

[Uses the Indifference Curve Approach] a. Draw a budget line for Rafaella, who has a weekly income of \(\$ 30 .\) Assume that she buys chicken and eggs, and that chicken costs \(\$ 5\) per pound while eggs cost \(\$ 1\) each. Add an indifference curve for Rafaella that is tangent to her budget line at the combination of 4 pounds of chicken and 10 eggs. b. Draw a new budget line for Rafaella, if the price of chicken falls to \(\$ 3\) per pound. Assume that Rafaella views chicken and eggs as substitutes. What will happen to her chicken consumption? What will happen to her egg consumption?

Short Answer

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After drawing Rafaella's initial budget line and indifference curve, we found that she would buy 4 pounds of chicken and 10 eggs to maximize her utility. Once the price of chicken drops to \$3 per pound, we draw a new budget line, which intersects the y-axis at 30 and x-axis at 10. Considering chicken and eggs as substitutes, Rafaella is now likely to increase her consumption of chicken due to the lower relative price in comparison to eggs and, conversely, reduce her egg consumption.

Step by step solution

01

Drawing the Initial Budget Line

On a graph where the x-axis is chicken and the y-axis is eggs, the initial budget line can be drawn by determining the maximum affordance for each good. The maximum amount of chicken Rafaella can buy is equal to her income divided by the price of chicken, which is \( \frac{30}{5}=6 \) pounds. The maximum amount of eggs is \( \frac{30}{1} = 30 \) eggs. Hence, the budget line will intersect the y-axis at 30 and the x-axis at 6.
02

Adding an Indifference Curve

An indifference curve shows all combinations of chicken and eggs that provide Rafaella with the same level of satisfaction. The curve is composed of points (combinations of goods) which Rafaella values equally. Rafaella's indifference curve in this case should be tangential to her budget line at the combination of 4 pounds of chicken and 10 eggs. This is an optimal consumption point where she maximizes her utility given her budget constraints.
03

Drawing the New Budget Line

The price of chicken falls to \$3 per pound. This changes Rafaella's budget line because she can now afford more chicken with the same income. The maximum amount of chicken she can buy now is \( \frac{30}{3}=10 \) pounds. Therefore, the new budget line will intersect the y-axis at 30 (as price of eggs has not changed) and the x-axis at 10.
04

Predicting Changes in Consumption

As Rafaella sees chicken and eggs as substitutes, a drop in the price of chicken encourages her to consume more chicken and less eggs. Her chicken consumption will increase and her egg consumption will decrease.

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Most popular questions from this chapter

Three people have the following individual demand schedules for Count Chocula cereal that show how many boxes each would purchase monthly at different prices: $$\begin{array}{lccc} \text { Price } & \text { Person 1 } & \text { Person 2 } & \text { Person 3 } \\\ \hline \$ 5.00 & 0 & 1 & 2 \\ \$ 4.50 & 0 & 2 & 3 \\ \$ 4.00 & 0 & 3 & 4 \\ \$ 3.50 & 1 & 3 & 5 \end{array}$$ a. What is the market demand schedule for this cereal? (Assume that these three people are the only buyers.) Draw the market demand curve. b. Why might the three people have different demand schedules?

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.

[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.

[Uses the Marginal Utility Approach] Now go back to the original assumptions of problem 1 (novels cost \(\$ 8,\) CDs cost \(\$ 6,\) and income is \(\$ 120\) ). Suppose that Parvez is spending \(\$ 120\) monthly on paperback novels and used CDs. For novels, \(M U / P=5 ;\) for CDs, \(M U / P=4 .\) Is he maximizing his utility? If not, should he consume (1) more novels and fewer CDs or (2) more CDs and fewer novels? Explain briefly.

[Uses the Indifference Curve Approach] Howard spends all of his income on magazines and novels. Illustrate each of the following situations on a graph, with the quantity of magazines on the vertical axis and the quantity of novels on the horizontal axis. Use two budget lines and two indifference curves on each graph. a. When the price of magazines rises, Howard buys fewer magazines and more novels. b. When Howard's income rises, he buys more magazines and more novels. c. When Howard's income rises, he buys more magazines but fewer novels.
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