Question

Suppose that Jones and Smith have each decided to allocate $1000 per year to an entertainment budget in the form of hockey games or rock concerts. They both like hockey games and rock concerts and will choose to consume positive quantities of both goods. However, they differ substantially in their preferences for these two forms of entertainment. Jones prefers hockey games to rock concerts, while Smith prefers rock concerts to hockey games.

a. Draw a set of indifference curves for Jones and a second set for Smith.

b. Using the concept of the marginal rate of substitution, explain why the two sets of curves are different from each other.

Short answer

a. IC for Jones:

IC for Smith:

b. The two different corner solutions give two sets of curves for Jones (indifference curve cuts y-axis and touches the budget line) and Smith (indifference curve cuts x-axis and touches the budget line).

Step-by-step solution

Jones and Smith’s indifference curves

Jones prefers hockey games to rock concerts. He will allocate $1000 for hockey games.

The above indifference curve depicts a corner solution for Jones, where he has zero allocations for a rock concert.

Smith chooses rock concerts to hockey games. He will allocate $1000 for rock concerts.

The above indifference curve depicts the corner solution for Smith, where he has zero allocations for hockey games.

Marginal rate of substitution and indifference curves

The consumption basket that lies on the highest indifference curve touching the budget line maximizes a consumer’s satisfaction.

The satisfaction is maximized when:

$MR{S}_{Hackey,Concert}=\frac{P_{Hockey}}{P_{Concert}}$

Jones’s marginal rate of substitution will be:

$MR{S}_{Concert,Hackey,}=\frac{P_{Concert}}{P_{Hockey}}=\frac{0}{1000}$

Smith’s marginal rate of substitution will be:

$MR{S}_{Hockey,Concert}=\frac{\$0}{\$1000}=0$

The marginal rate of substitution calculations for Jones and Smith show that MRS becomes zero when price ratios are reversed. This means that the indifference curve is tangent to the budget line and cuts the y-axis (Hockey games) for Jones. While the indifference curve is tangent to budget line cuts x-axis (rock concert) in the case of Smith.