Q3[50 points] Sylvia's utility function over waffle fries, F, and frozen yogurt, Y is given

by = 2 . Her marginal utility from waffle fries is = 2, and her marginal

utility from frozen yogurt is = 2. A pack of frozen waffle fries sells for $4. The price

of a cup of frozen yogurt is $6. Sylvia has budget of $120 to allocate to these items each

month.

a) For Sylvia's utility functions above, draw a set of indifference curves showing utility levels U = 20, U = 30, and U = 40

b) What is the equation for Sylvia's budget line. Draw it (with frozen yogurt -Y- on the vertical axis), and label the slope and intercepts.

c) What is the Sylvia's marginal rate of substitution?

d) If Sylvia maximizes her utility, how much of each food should she consume? Solve for her optimal bundle. Show how to determine this bundle on a diagram using indifference curves and a budget line.

e) Briefly explain if each of the four conditions of the utility maximizing behavior is satisfied with the bundle you have obtained in (d).

f) Now suppose that Sylvia's monthly waffle fries and frozen yogurt is $180? Solve for her optimal bundle. Show how to determine this bundle on a diagram using indifference curves and a budget line.