Price Theory

Assignment 1 – Consumer Theory

Suppose that Sally’s preferences over baskets containing food (good x), and clothing (good y), are described by the utility function U(x, y) =

√ x + y. Sally’s corresponding marginal

utilities are,

MUx = 1

2 √ x

and MUy = 1.

Use Px to represent the price of food, Py to represent the price of clothing, and I to represent Sally’s income.

Question 1: Find Sally’s food demand function, and Sally’s clothing demand function. For the purposes of this question you should assume that I/Py ≥ Py/4Px. (7 Marks)

Question 2: Describe the relationship between Sally’s demand for food and,

(a) Sally’s income;

(b) the price of food;

(c) the price of clothing.

Your answers should reference the demand function that you derived in question 1, and correctly apply the relevant terminology. You should continue to assume that I/Py ≥ Py/4Px. (6 Marks)

Question 3: Now assume that I/Py < Py/4Px. Find Sally’s food demand function, and Sally’s clothing demand function. (4 Marks)

Question 4: Suppose that the price of clothing is Py = $50 per item, and that Sally’s income is I = $425. What are the income and substitution effects if the price of food increases from Px1 = $5 per meal, to Px2 = $12.50 per meal? (8 Marks)

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