Consider the utility-maximizing model in a two-good world, where our representative consumer has well-behaved preferences that result in smooth indifference curves that are convex to the origin. Place good one on the horizontal axis. (Assume I=$120 and P1=$3 and P2=$4
a. Illustrate utility maximization where the consumer purchases positive quantities of both goods.
b. Show the effect a $2 excise tax levied on good one has on the consumer’s utility-maximizing bundle (assume the $2 tax results in a $2 increase in price).
c. Assume consumers purchase 10 units of good one with the $2 excise tax. Rather than imposing the excise tax, the government could levy a $20 income tax, and raise the same tax revenue. Compare the effects the income tax and the excise tax have on the consumer’s utility. Under which plan (excise or income tax) is utility higher? Provide a graph and explain your finding.
d. Compare your answer in part c, with the case where goods one and two are perfect complements. Illustrate and explain your answer.