Describe the relationship between sallys demand for food

Question

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,

MU_x = 1 / 2√x and MU_y = 1.

Use P_x to represent the price of food, P_y 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 / P_y  ≥ P_y / 4P_x.

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 / P_y  ≥ P_y / 4P_x.

Question 3: Now assume that I / P_y  ≥ P_y / 4P_x. Find Sally's food demand function, and Sally's clothing demand function.

Question 4: Suppose that the price of clothing is P_y = $50 per item, and that Sally's income is I = $425. What are the income and substitution eects if the price of food increases from P_x1 = $5 per meal, to P_x2 = $12:50 per meal?