Question

a) At the supermarket, milk costs $2 per quart while cereal costs $5 per box.

1. In a diagram, measuring quarts of milk along the horizontal axis, draw the budget constraint of a consumer with an overall cash budget of $20.

2. In the diagram, illustrate how the consumer’s budget constraint changes if there is a two-for-one sale on cereal.

3. In the diagram, illustrate how the consumer’s budget constraint changes if the two-for-one sale on cereal applies only to the first 4 boxes.

b) A high-school student has a monthly budget of $80 to spend on music and burritos. Burritos cost $8 each, while songs are free after paying the Spotify monthly fee of $9.99.

1. In a diagram, measuring songs along the horizontal axis, draw the high-school student’s budget constraint.

c) A family has an yearly income of $50,000 to spend on the kids’ education or on all other goods.

1. In a diagram measuring dollars spent on education along the horizontal axis and dollars spent on all other goods along the vertical axis, draw the family’s budget constraint.

2. In your diagram, draw the family’s budget constraint if the family must pay a 10% income tax but receives a $5,000 school voucher.

Answer 1

(a) 1. Cost of milk () is $2 and cost of cereal () is $5.

The cash budget is 20$. Hence, the equation of budget constraint is , for x represents milk and its quantity and y represents cereal and its quantity. The graph is as below.

Here, milk is plotted on x-axis while cereal on y-axis. The maximum of milk that can be bought is for y (cereal) is zero, ie or units, while maximum of y can be analogously found as 4 units. The budget line joins these intercepts on x and y axis.

2. If there is a 2 for 1 sale, ie buy 2 cereal and get 1 free, then the new price of 3 units of cereal is equal to the old price of 2 cereal, ie or or . In that case, the new budget line will be as . The graph of this is shown as below.

Here, the purchasing power has increased as price of y has decreased, and the maximum of y can be bought as 6 units.

3. It is a bit tricky. In the old budget line, the maximum of y that could be bought was 4 units. So, even if the sale offer is for first 4, the price change will be same as that of part-2 of the question. Hence, there would be no change, the new budget line is what still affordable to the consumer. Think it like that with the price of cereal $5, the consumer could only bought a maximum of 4 units, and with the sale price, the consumer can have 6 units by buying 4 units. So, there would be no change if maximum sale limit was 4 units, for which consumer will still buy a maximum of 4 and get a total of 6 units.