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 x ¯2 (that is, consumption of good 2 up to quantity x ¯2 is exempt of tax). Denote by t the amount of dollars a consumer has to pay for every unity she consumes in excess of x ¯2.
Draw the budget set of a consumer with income m. Is the slope of the budget line constant?