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.