3. Susan has the following utility function U(x,y) = xy, where x represents food and y represents other goods. Susan has £20 (budget m) to spend on these two goods. Suppose that the initial price of x (Px) is £1 per unit, and that of y (Py) is £1 per unit. Note that MUx=y and MUy=x. (i) How many units of x and y will Susan purchase? Assuming that Px varies and m and Py stay constant at the values £20 and £2, respectively, what is the individual demand function for x? (ii) What are the characteristics the individual demand function for x? What is its aggregate counterpart, and what is its economic importance?
3. Susan has the following utility function U(x,y) = xy, where x represents food and y represents other goods. Susan has £20 (budget m) to spend on these two goods. Suppose that the initial price of x (Px) is £1 per unit, and that of y (Py) is £1 per unit. Note that MUx=y and MUy=x. (i) How many units of x and y will Susan purchase? Assuming that Px varies and m and Py stay constant at the values £20 and £2, respectively, what is the individual demand function for x? (ii) What are the characteristics the individual demand function for x? What is its aggregate counterpart, and what is its economic importance?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:3. Susan has the following utility function \(U(x,y) = xy\), where \(x\) represents food and \(y\) represents other goods. Susan has £20 (budget \(m\)) to spend on these two goods. Suppose that the initial price of \(x\) \((P_x)\) is £1 per unit, and that of \(y\) \((P_y)\) is £1 per unit. Note that \(MU_x = y\) and \(MU_y = x\).
(i) How many units of \(x\) and \(y\) will Susan purchase? Assuming that \(P_x\) varies and \(m\) and \(P_y\) stay constant at the values £20 and £2, respectively, what is the individual demand function for \(x\)?
(ii) What are the characteristics of the individual demand function for \(x\)? What is its aggregate counterpart, and what is its economic importance?
(20 marks)
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