Question

Sylvia’s utility function over waffle fries, F, and frozen yogurt, Y is given by U = 2 ∗ F ∗ Y. Her marginal utility from waffle fries is MUF = 2Y, and her marginal utility from frozen yogurt is MUY = 2F. 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.

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

SOMEONE PREVIOUSLY ANSWERED QUESTION D, BUT I NEED HELP WITH QUESTION E AND F, THE LINK TO ANSWER D: https://www.chegg.com/homework-help/questions-and-answers/sylvia-s-utility-function-waffle-fries-f-frozen-yogurt-y-given-u-2-f-y-marginal-utility-wa-q50865827?trackid=KtTaoYDi

Answer 1

Answer e: Yes, it does satisfy all the four assumption of Utility maximization . Here the consumer equalizes the marginal utility with respect to price for the the two goods under consideration.The budget mention for the two goods is pre defined that is $120 which is the second assumption.The consumer can rank their preference thus bundle of goods can be selected which is the third assumption. The price of the goods is considered during the selection of bundle as it can be revailed through bundle itself it is the fourth assumtion. Thus each and ever condition is fully satisfied.

Answer f: Given U= 2 F Y, MUF=2Y, MUY=2F, Price(F)=$4, Price(Y)= $6, Budget=$ 180

MUF/P(F)= (2Y)/4 MUY/P(Y)= (2F)/6 Budget line= 4F + 6Y = 180

   MUF/P(F)=MUY/P(Y) =2F + 3Y = 90

2Y / 4= 2F / 6, Y=(2/3) F .......(i)

Using the value of (i) in the budget line we get 2F + 3( 2F/3)= 90

F= 22.5=23(approx)

Using the value of F we get Y= 15

Thus the Optimal bundle (23,15).

The indifference curve and the budget line is shown in the following diagram the bundle combination is shown by the blue line.