Suppose preferences are characterized by the utility function u(x1, x2) = x1x22. As usual, the budget constraint is p1x1 + p2x2 = m.

To be concrete, suppose p1 = p2 = 10 and m = $90.

1. Now suppose the government places a 50% tax on x1. Write the new budget constraint, given this tax. Identify the utility maximizing bundle of x1 and x2 for Alice, the amount of tax revenue collected by the government, and calculate Alice's utility. Ignore second-order conditions.

2. Now suppose instead the government places a 20% taxon x2. Once again, write the new budget constraint, given this tax.Identify the utility maximizing bundle of x1 and x2 for Alice, theamount of tax revenue collected by the government, and calculateAlice's utility. Ignore second-order conditions.

3. In light of your answers to [3.1] and [3.2], which of thetwo tax policies considered in those parts would you recommend tothe government? Why?