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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,

1

and MUy = 1.

MUx = ?

2 x

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 &lt; 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)

1

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