Problem 3 Consumer's Problem
This problem is designed to help you see why economists typically draw downward sloping demand curves.
(a) given that tastes are rational, strictly monotone, strictly convex, and continuous, under what unlikely conditions will individual demand curves be upward sloping? (hint: refer the direction and relative size of income and substitution effects)
(b) Assuming preferences are homothetic in x1 and $otherCons and tastes are rational, strictly monotone, strictly convex, and continuous, graphically derive the consumer's demand curve for x1. Is it downward sloping?
(c) Assuming preferences are quasilinear in X1 and $otherCons (where X1 is the quasilinear good) and tastes are rational, strictly monotone, strictly convex, and continuous, graphically derive the consumer's demand curve for x1. Is it downward sloping?
(d) In which case is the demand curve steeper? why?
(e) How do the price elasticities of demand compare for the two demand curves? Which is larger in absolute value?

Problem 4
Consumer demand assuming tastes are rational, strictly monotone, strictly convex, and continuous
(a) Use graphs to derive the demand curve for beer assuming tastes for beer versus other consumption are homothetic.
(b) Use graphs to derive the demand curve for beer assuming tastes for beer versus other consumption are quasilinear (ie. beer is a quasilinear good).
(c) How do the demand curves in parts a and b compare? Why? (think in terms of substitution and income effects)
(d) In which case is the demand curve steeper? why?
(e) In which case is the quantity of beer demand more sensitive to price changes?
(f) How do the price elasticities of beer demand compare for the two demand curves? Which is larger in absolute value?
(g) Under what unlikely conditions would the demand curve for beer be upward sloping?

Problem 3 Consumer's Problem This problem is designed to help you...