Question

A consumer lives on a diet of solely steak and potatoes. Her budget is \(30 for every 10 days, and she must buy enough potatoes to eat at least two potatoes per day.

a. A potato costs \)0.50 and the price of a steak is \(10.How much will the consumer purchase of each good?

b. Now suppose that the price of potato increases to \)1. How much will the consumer purchase of each good?

c. Now suppose that the price of potato increases to $1.25. How much will the consumer purchase of each good?

d. What kind of good is the potato?

e. Would you expect the demand curve for potatoes to continue to follow this trend indefinitely? Why or why not?

Short answer

a. The consumer will buy 20 units of potatoes and 2 units of steak for 10 days.

b. The consumer will buy 20 units of potatoes and 1 unit of steak for 10 days.

c. The consumer will buy 20 units of potatoes and 0.5 units of stake for 10 days.

d. Potato is a Giffen good.

e. The demand curve for potatoes will not continue to follow this trend indefinitely, since once potatoes exhaust all the income of the consumer, the consumer will reduce their consumption.

Step-by-step solution

Explanation for part (a)

The consumer has a budget of $30 for 10 days. The prices of two goods that the consumer consumes, potatoes and steak, are given as $0.50 and $10 per unit for each good, respectively.

Thus, the budget constraint will be:0.50P+10S=30, where P is the quantity of potatoes consumed, and S is the quantity of steak consumed.

Since the minimum number of potatoes per day is 2, for a 10-day diet, it will be 20 potatoes. Thus given his income for 10 days, his consumption will be:

$$\begin{gathered} 0.50P+10S=30 \\ 0.50\left(20\right)+10S=30 \\ 10S=30-10 \\ S=\frac{20}{10}=2 \end{gathered}$$

Thus, P=20 and S=2.

Explanation for part (b)

If the prices of the potatoes change to $1 while the income remains the same, the consumption of the consumer will be as follows:

$$\begin{gathered} 1P+10S=30 \\ 20P+10S=30 \\ 10S=30-20 \\ S=\frac{10}{10}=1 \end{gathered}$$

Thus, P=20 and S=1.

The consumer cannot reduce his consumption of potatoes since he needs to consume 2 potatoes per day. Thus, given budget constraints, he must reduce his consumption of steak by one unit.

Explanation for part (c)

If the price of potatoes changes to $1.25, the consumption of the consumer will become:

$$\begin{gathered} 1.25P+10S=30 \\ 1.25\left(20\right)+10S=30 \\ 10S=30-25 \\ S=\frac{5}{10}=0.5 \end{gathered}$$

P=20 and S=0.5

The consumer must consume 20 units of potatoes and his income is constant, $30 for 10 days. He needs to reduce his steak consumption further to 0.5.

Explanation for part (d)

Potatoes are Giffen goods. Giffen goods are non-luxuries goods that violate the law of demand and establish a positive relationship between the price and the demand. The consumption of these goods keeps on increasing as the prices of these goods increase.

Giffen goods can be regarded as inferior goods that people consume the very low level of income. These goods are staples for these poor people and take a major portion of their income.

Explanation for part (e)

It does not mean that the demand curve for Giffen goods, i.e., potatoes, would keep sloping upward indefinitely. There will be a point where the prices of these goods become so high that it drains all of the consumer's income. At this point, the consumer starts decreasing his consumption of these goods if there is any further price increase.

The graph above shows income on the y-axis and quantity demanded on the x-axis. As long as the prices remain under the budget or income of the consumer, that is $30, the demand for the potatoes will increase, as shown in the graph. Once the prices of potatoes increase so much that it drains all the consumer's income, any further increase will bend the demand curve backward.