Rachel's preferences for goods x and y are represented by the following utility function: U(QX, QY ) = Q 1/4 X Q 3/4 Y .
(a) Find the expression of the marginal rate of substitution in terms of QX and QY . Comment whether it is increasing, constant or decreasing in QX.
(b) Find the utility level and plot the associated indifference curve for each of the following bundles, A: (48,3) and B: (9,9).
(c) Now find a bundle on the second indifference curve, which has the same slope as the first indifference curve through point A (48,3).
(d) Assume that QY = 1. Graph U(QX, 1) as a function of QX.
(e) Assume that QY = 1. Graph MUQX (QX, 1) as a function of QX.
(f) Now assume that the price of good x is px = 3 and the price of good y is py = 2. We also know that Rachels income is I = 24. Find her optimal bundle, the associated utility level and plot the budget constraint and indifference curve, clearly marking her optimal bundle.