In: Economics
The utility that Jane receives by consuming good X and good Y is given by u(X,Y) = XY.
5.1) Draw the indifference curve associated with a utility level of 12 and the indifference curve associated with the utility level of 36.
5.2) Suppose that X costs $1 per unit and Y $3 per unit. Jane has $12 to spend on X and Y. Graph the budget line that she faces.
5.3) Derive Jane’s demand functions. What is the utility-maximizing choice of X and Y (solve the problem both mathematically and graphically).
5.4) What is the marginal rate of substitution of X for Y when utility is maximized? Give a concise explanation of the meaning of the marginal rate of substitution.
5.5) Suppose Jane buys 3 units of X and 3 units of Y with her $12 budget. What is her MRS of X for Y? What is she willing to do to have her MRS equal to the price ratio?
5.6) Suppose the price of X increases to $2, X=3 and Y=3. How much extra income does the agent need to compensate her for the price rise, so that the original bundle is affordable?