1. Suppose a consumer's utility is given by U = 4X + 2Y .

(a) Suppose the consumer is currently consuming optimally, with some positive amount of X and a positive amount of Y . What must the ratio of prices be? In other words, what must PX PY be equal to?

2. Suppose a consumer has utility given by U = XY and faces the budget constraint 5X + 2Y = 50.

(a) Solve for the consumer's optimal bundle, (X , Y ). Find the consumer's level of utility at this optimal bundle

(b) Now assume the price of Y falls to $1. Solve for the new optimal consumption bundle.

3. If income elasticity of demand is 0.8 and income increases by 2%, by what percent does quantity demanded change?

4. If X is a normal good and the price of Y falls, is the substitution effect positive or negative? Is the income effect positive or negative? What if X is an inferior good?