An agent consumes goods $x$ and $y$, with prices $P _ { x } = \$ 5$ per unit and $P _ { y } = \$ 8$ per unit. The consumer's income is $I = \$ 48$. The government imposes a tax of $\$ 1$ per unit on good $x$. What is the new equation for the budget constraint?
A) $y = 6 - ( 5 / 8 ) x$
B) $y = 6 - .75 x$
C) $y = 8 - ( 6 / 8 ) x$
D) $y = 48 - 8 x$

Question

Quizplus · Accepted Answer

After the tax is imposed, the price of good $x$ increases to $\$6$, as the tax of $\$1$ per unit is added to the original price of $\$5$. This results in the following budget constraint: $$5x + 8y = 48$$ $$6x + 8y = 48$$ $$y = 6 - (3/4)x$$ Therefore, the best choice is option B. To maximize utility, the agent will choose the combination of goods that falls on the highest possible indifference curve that is tangent to the new budget constraint. With the tax of $\$ 1$ per unit on good $x$, its price increases to $\$ 6$ per unit. The new equation for the budget constraint is $5x + 8y = 48 - x \Rightarrow 6x + 8y = 48 \Rightarrow 3x + 4y = 24$. Solving this equation for $y$ gives us $y = (6/8)x + 3/2$, which simplifies to $y = 0.75x + 1.5$. Therefore, the best choice is B, as it matches the equation for the new budget constraint. To maximize utility, the consumer will choose the combination of goods that lies on this budget constraint and gives the highest level of satisfaction.

An Agent Consumes Goods xxx And yyy , with Prices Px=$5P _ { x } = \$ 5Px​=$5

An Agent Consumes Goods $x$ And $y$ , with Prices $P _ { x } = \$ 5$