Question

A recent newspaper circular advertised the following special on tires: “Buy three, get the fourth tire for free—limit one free tire per customer.” If a consumer has $\mathbf{\backslash (}\mathbf{360}$to spend on tires and other goods and each tire usually sells for$\mathbf{\backslash )}\mathbf{40}$, how does this deal impact the consumer’s opportunity set?

Short answer

The consumer’s opportunity set will still be the same even after he gets the offer of "Buy three, get the fourth tire free - limit one free tire per customer."

Step-by-step solution

Finding the horizontal and vertical intercept

Use the following equation,

$X=\frac{M}{P_x}$

Here,

$M$is the Total Income

$X$is the Maximum Quantity of Tiers.

$P_x$is the Price of the Tier

$\mathrm{M}=\mathrm{\$}360$

${\mathrm{P}}_{\mathrm{x}}=\mathrm{\$}40$

By substituting we will get,

$\begin{array}{c}X=\frac{M}{P_x}\\ =\frac{\$360}{\$40}\\ =9\end{array}$

Therefore, the maximum quantity that is affordable of the tiers is$9$units, it is the horizontal intercept of the budget line.

Using the equation again;

$Y=\frac{M}{P_y}$

Here,

$M$is the Total income

$Y$is the Maximum Quantity of Other goods.

$P_y$is the Price of the Tier

$\mathrm{M}=\mathrm{\$}360$

${\mathrm{P}}_{\mathrm{y}}=\mathrm{\$}1$

By substituting we will get,

$\begin{array}{c}\mathrm{Y}=\frac{\mathrm{M}}{{\mathrm{P}}_{\mathrm{y}}}\\ =\frac{\mathrm{\$}360}{\mathrm{\$}1}\\ =360\end{array}$

Therefore, the maximum quantity that is affordable of the other goods is$360$ units, it is the vertical intercept of the budget line.

Plot the graph

Plot the graph with the offer

Here, tire offer was promoted in a recent newspaper circular: "Buy three, get the fourth tire free-limit one free tire per customer." Therefore, the maximum tier that he can buy is$10$units while the maximum quantity that he can purchase for all the other goods remain at $360$.

Thus, looking at the graph, we can say that the opportunity set will still remain the same if customer will get the offer of "Buy three, get the fourth tire free -limit one free tire per customer." when it is shifted to the right.