A consumer's utility function over cars and housing is given by U(C, H) = 30 + 4log(H). The prices of food and housing are PC = $120 and PH = $80, and the consumer's income is Y = $220. 2.1 Derive the consumer's optimal bundle of cars and housing. [3] 2.2 For what values of the consumer's income will the consmner choose a positive quantity of cars? Of housing? [3] 2.3 Derive expressions for the consumer's Engel curves for cars and housing anti plot them. (Hint: the functions may be diEFerent over different ranges of Y.) [3]