Suppose the government wishes to tax a utility-maximizing consumer to obtain a certain amount of tax revenue. A utility maximizing consumer has utility function u(x, y) = x + y. The price of x is $1, the price of is $4 and his income is $120.

a) Suppose the government imposes sales tax t = 1 on good x per unit. What is the optimal consumption for good x and good y for the consumer under the sales tax? What is the utility level that the consumer achieves under the sales tax? How much revenue does the government collect by imposing sales tax?

b) Does the sales tax produce deadweight loss? If it does, calculate the deadweight loss generated by the sales tax.