Question 2 A consumer's utility function over cars and housing is given by U (C, H) = 30 + 4 log(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 consumer choose a positive quantity of cars? Of housing? [3] 2.3 Derive expressions for the consumer's Engel curves for cars and housing and plot them. (Hint: the functions may be different over different ranges of Y.) [3]