Suppose a consumer is trying to make a choice over the consumption of two goods: x and y. Px =...


Suppose a consumer is trying to make a choice over the consumption of two goods: {eq}x {/eq} and {eq}y {/eq}. {eq}P_x {/eq} = $3, {eq}P_y {/eq} = $4, and the income is equal to $50. Assume that the government distributes some stamps that are good to buy 5 units of good {eq}x {/eq}. Write down the formula for the budget constraint. What happens if we allow for the stamps to be traded at a price equal to $1?

Food Stamps

Food stamps are often provided by the government, especially to the low-income families in a country. The low-income families use those stamps to purchase costly items at a very cheap price, for which their total expenses also get reduced.

Answer and Explanation: 1

With $50 as income, the budget constraint of the consumer when the price of good x is $3 is shown below:

{eq}\begin{align*} Income &= {{\mathop{\rm P}\nolimits} _x}x + {{\mathop{\rm P}\nolimits} _y}y\\ \$ 50 &= 3x + 4y \end{align*} {/eq}

When the food stamps are introduced here, it can allow the consumer to purchase 5 units of x at $1, which is the cost of the stamp. Therefore, the price of one unit of x from the viewpoint of the stamp buyers will get reduced to 0.2, which can be found by dividing $1 by 5 units, and the corresponding budget constraint is shown below.

{eq}\begin{align*} \$ 50 &= \dfrac{1}{5}x + 4y\\ \$ 50 &= 0.2x + 4y \end{align*} {/eq}

It can be envisaged that the consumer can purchase more units of x if the consumer purchases the stamp by incurring $1.

Learn more about this topic:

Budget Constraints: Definition & Formula


Chapter 1 / Lesson 6

Learn what budget constraint is and view examples. Understand how to use the budget constraint formula and how to represent a budget constraint using a graph.

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