Question

The price of a pound of rice is 1 dollar, and the price of a pound of sugar is 2 dollars. Jeff only buys rice and sugar, and has 50 dollars of income to spend. He spends it all on either rice or sugar. Sketch the budget line for Jeff, who plans to spend 50 dollars on some combination of rice and sugar. Add an indifference curve (label it IC1) assuming his optimal combination is 20 units of rice. (Hint: you have to find the other point on the IC for sugar) Suppose that the government levies a 25% tax on sugar, whereas price of rice remains the same. Show the effect on the budget line and add a new indifference curve (label it IC2) assuming the optimal combination is now 25 units of rice. (Hint: you have to find the other point on the IC for sugar). What are the tax revenues to the government? If equivalent variation is 10 dollars what is the excess burden? Is this tax efficient?

Answer 1

Budget line is the line showing the combinations of two goods that a consumer can purchase with a given income or budget. The budget line shows all those combinations of the two goods available to the consumer. In our question, the price of a pound of rice is 1 dollar, and the price of a pound of sugar is 2 dollars. Jeff only buys rice and sugar, and has 50 dollars of income to spend. He spends it all on either rice or sugar.

In the above figure, units of sugar is depicted on the x axis and units of rice is depicted on the y axis. Figure shows the budget line for Jeff, who plans to spend 50 dollars on some combination of rice and sugar.

If Jeff spends him entire income 50 dollars on rice, he can buy 50 pounds of rice since a pound of rice is 1 dollar. If he spends him entire income 50 dollars on sugar, he can buy 25 pounds of sugar since a pound of sugar is 2 dollars.

An indifference curve is the locus of the combinations of two goods that yields the same level of satisfaction or utility to the consumer. Since all points on indifference curve yield the same satisfaction to the consumer it can also be called an isoutility curve. The consumer is indifferent between the combinations indicated by any two points on the same indifference curve.

In the above figure, units of sugar is depicted on the x axis and units of rice is depicted on the y axis. The indifference curve (C1) will be an optimal combination is 20 units of rice which tangents the budget line at the point A. Actually, at this point A, Jeff spends his entire income on 20 pounds of rice and 15 pounds of sugar.

That is,

20 units of rice x 1 dollar = 20

15 units of sugar x 2 dollars = 30

20 + 30 = 50 dollars (which is equal to his income)

When the government levies a 25% tax on sugar, the price of sugar per unit, increases from 2 dollars to 2.5 dollars. With a same price of rice and with an increase in the price of sugar, the new budget line will be BL2 in the figure which is left to the previous budget line.

The effect on the budget line with the optimal combination of 25 units of rice is depicted by a new indifference curve (IC2) which tangents the new budget line at point B.

At this point of tangency between new budget line and indifference curve, Jeff purchases an optimal combination of 25 units of rice and 10 units of sugar.

That is,

25 units of rice x 1 dollar = 25

10 units of sugar x 2.5 dollars = 25

25 + 25 = 50 dollars (which is equal to his income)

The tax revenues to the government

When the government levies a 25% tax on sugar, the price of sugar per unit, increases from 2 dollars to 2.5 dollars and the tax per unit of sugar is 0.5 dollar. After the tax, Jeff purchases 10 units of sugar. Thus, the tax revenues to the government will be

10 units of sugar x 0.5 dollar = 5 dollars

In economics, equivalent variation refers to the change in income required to bring the consumer's utility level equal to the level that would occur in case the event had happened. If equivalent variation is 10 dollars the excess burden will be 5 dollars and the tax is efficient here.