If the government imposes a quantity tax on the consumption of a good, it
means that the consumer has to pay for each unit of the good its price plus
the tax. For example, if the price of a chocolate bar is $5 and the government
imposes a tax of 20 cents on the consumption of a chocolate bar, then the
actual price the consumer pays for a chocolate bar is $5 + $0.2 = $5.20.
Suppose there are two goods available for consumption, good 1 and good
2, and that the government taxes consumption of good 2 that is in excess
of quantity x2 (that is, consumption of good 2 up to quantity x2 is exempt
of tax). Denote by t the amount of dollars a consumer has to pay for every
unity she consumes in excess of x2.
Draw the budget set of a consumer with income m. Is the slope of the
budget line constant?
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To draw the budget set of a consumer with income m, we need to consider the prices of both goods (p1 and p2), the quantity tax rate (t), and the quantity exemption (x2).
The budget line represents all the combinations of goods 1 and 2 that the consumer can afford with their given income. It can be expressed by the equation:
p1 * q1 + p2 * q2 = m
Where q1 and q2 represent the quantities consumed of goods 1 and 2, respectively.
Now, let's consider the case of good 2, which is taxed for consumption beyond x2 units. If the consumer consumes up to x2 units, the price paid will be p2. However, for consumption beyond x2 units, the consumer will have to pay an additional amount of t dollars for each unit consumed.
Therefore, if the consumer consumes q2 units of good 2, the price paid for good 2 will be:
p2 * q2, if q2 <= x2
(p2 * x2) + (t * (q2 - x2)), if q2 > x2
Given this information, we can draw the budget set on a graph by plotting the quantity of good 1 (q1) on the x-axis and the quantity of good 2 (q2) on the y-axis.
The slope of the budget line represents the rate at which the consumer can trade one good for another while staying within their budget constraint. In this case, assuming prices do not change, the slope of the budget line will be equal to -p1/p2.
However, note that the slope of the budget line will change beyond the quantity exemption (x2) for good 2. This is because the price paid for good 2 increases by t dollars for each additional unit consumed beyond x2. As a result, the slope of the budget line will increase as the consumer consumes more units of good 2 beyond x2.