Intermediate microeconomics questions

Econ 102 Intermediate Microeconomics Assignment # 3 (DueApril 19, in the class)

Part 1

Utility function from consuming a bundle of goods (X, Y) is given as U=X1/2Y1/2 and Prices are given as P= (PX, PY) = ($2, $4), and income M= $100

1. Derive the optimum consumption bundle.

2. If Prices now change to P’= (PX’, PY’) = ($4, $4). Derive the new optimum consumption bundle, and the substitution effects on the consumption of each goods.

3. Under the new prices, what are the income effects on the consumption of each goods?

4. Graphically show the price effect, substitution effect and income effect on the consumption of goods X.

Part 2

Employ the idea of Slustky Equation to answer the following questions:

1. Define normal goods, inferior goods and Giffen goods.

2. Using Slutsky Equation to explain why the price effect on normal goods has to be negative?

3. Why the demand for Giffen goods increases when its price goes up?