Question - Consumer choice problems (duality) II Individuals consume three breakfast goods - cereal q1, bacon q2 and eggs q3.

Preferences are modelled by an indirect utility function v(p1, p2, p3, y) = y/ Root(p1(p2+p3)) , where y denotes total breakfast spending and (p1, p2, p3) are the prices of the three goods.

1. What is the expenditure function?

2. What are the Hicksian demands?

3. What are the Marshallian demands?

4. Are preferences homothetic? How can you tell?

5. Assume prices are given by (p1, p2, p3) = (2, 2, 4) and total budget is given by y = 24.

(a) What are the utility-maximising consumption levels for goods 1,2 and 3, subject to the budget constraint?

(b) How much would the consumer spend on this utility-maximising bundle?

(c) What would be her utility from consuming the utility-maximising bundle?

6. What would be the answers to question 5) if the consumer's income were halved, i.e. if her total budget were now given by y = 12?