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Exercise 8.21 Quasilinear Utility Peter enjoys cereal and raisins. His preference relation can be represented by the following utility function: U(c, r) = 3 log(c) + r Assume that the price of a pound of cereal is 5 dollars and the price of a pound of raisins is 4 dollars. Additionally, assume that Peter has an income of 60 dollars.Suppose, now, that the price of cereal falls to 4 dollars per pound of cereal. d. Suppose that Peter pays a lump sum of money to be able to purchase cereal at the lewer price, such that he can still barely afford his original consumption bundle. What would his new income level be? How many pounds of cereal and pounds of raisins doel Peter buy at the lower price of cereal and his new income? Plot the new budget line in red ink and label the new Optimal bundle, Point 03. e. Suppose, now, that instead of being paying enough money to barely afford his orig'nal bundle, Peter pays enough money so he can still barely achieve the same level of utility as before the change in price. What would his new income level be? How many pounds of cereal and pounds of raisins docs Peter buy at the lower price of cereal and his new income? Plot the new budget line in red ink and label the new optimal bundle, Point 03. f. How many pounds of cereal and pounds of raisins does Peter consume at the nevi1r prices and his original income? How does this bundle compare to the results from parts (:1) and (e)? What changes? What doesn't? g. Draw this new budget line in blue ink and label the new optimal consumption bundle, point F. h. Comment on the relative magnitudes of the substitution and income own-price effects for this type of utility function. What is the general name for Peter's utility representation