7. Regan's utility function for toothpaste (good x) and other stuff (good y) is u(r,y) = Inx + y. Assume that p, = 1. Let M be her income. Derive her demand function for toothpaste. Is toothpaste a normal or an inferior good for Regan? Graph the Engel curve for p, = 1. 8. Continuing with Regan's behavior from Exercise 7 above, suppose now that M = 10 and that p, = 1/2. (a) What is Regan's optimal choice? (b) Find Regan's standard demand function and her compensated demand func- tion for toothpaste, in this situation. (c) Suppose the price of toothpaste goes down to 1/3. Calculate Regan's welfare change using the difference in her utility levels, and compare it to what you would get using the notion of consumer's surplus