2. Suppose Sharon has the following quasilinear utility function from candy x and other stuff M: U(x, M) = 20 M. The price per unit of candy is $p, and the price of other stuff is $1 per unit. Sharon has an income of Y = 100. Assume that candy is a continuous good. (a) Assuming an interior solution, show that Sharon's optimal quantity of x is x* = why p must be great than 1 for the optimum to be interior. 100 p2 Explain (b) If instead p 1, then Sharon has a corner solution. At this corner solution, what is her consump- tion of M and x, as a function of p? (c) Sketch Sharon's demand curve for candy. Given a price of p, how is Sharon's consumer surplus defined? Feel free to use your diagram as an explanation, but give a precise verbal definition as well. The government has decided to apply a sales tax on candy of 0.5 per unit of candy. The price of candy before the tax was po = 2 and so the price of candy after the tax is p = 2.5. It can be shown by integration of Sharon's demand curve, that her consumer surplus as a function of price is given by CS(p) = as long as p 1. 100 P (d) Using consumer surplus as a welfare measure, what is the Sharon's welfare loss due to the tax?