Use the table below to answer the following questions. The table contains the marginal rates of substitutions at different quantities of two goods (x and y) for different levels of utility-this is a table of the indifference curves in the graph below. The table uses the utility function U=(XY)½ which yields indifference curves of the form Y=U2/X.
U=2 U=3 U=4 U=6
X Y MRS X Y MRS X Y MRS X Y MRS
1 4.00 4.00 1 9.00 9.00 1 16.00 16.00 1 36.00 36.00
2 2.00 1.00 2 4.50 2.25 2 8.00 4.00 2 18.00 9.00
3 1.33 0.44 3 3.00 1.00 3 5.33 1.78 3 12.00 4.00
4 1.00 0.25 4 2.25 0.56 4 4.00 1.00 4 9.00 2.25
5 0.80 0.16 5 1.80 0.36 5 3.20 0.64 5 7.20 1.44
6 0.67 0.11 6 1.50 0.25 6 2.67 0.44 6 6.00 1.00
7 0.57 0.08 7 1.29 0.18 7 2.29 0.33 7 5.14 0.73
8 0.50 0.06 8 1.13 0.14 8 2.00 0.25 8 4.50 0.56
a. Write and graph the equation for the budget constraint if M=48 and Px=8 and Py=8.
b. What is the utility maximizing bundle of x and y given this budget constraint? What is the consumer's level of utility? Add a representative convex indifference curve showing this bundle to your graph.
c. If M doubles to 96, how much will the consumer purchase of each good? What is the new level of utility? Add the new budget constraint, utility maximizing bundle, and a representative indifference curve to your graph.
d. Draw the income expansion path.
e. With M=48, how much will the consumer purchase of each good if the price of y falls so Py=2? Add the new budget constraint, utility maximizing bundle and a representative indifference curve to your graph.