Question

In: Economics

Roli loves to read and has a large dog. She consumes only two goods—books (B) and bags of dog food (F). Her utility function is given by:

Roli loves to read and has a large dog. She consumes only two goods—books (B) and bags of dog food (F). Her utility function is given by:

U = U(B, F) = 4B0.5F0.5

If Roli’s income is equal to $750/week and the price of a book (Pb) is equal to $25 and the price of a bag of dog food (Pf ) is equal to $50, how many books and bags of dog food should Roli purchase to maximize her utility? Note: She can buy full bags and partial bags of dog food.

At her optimal market basket, how many bags of dog food (F) would Roli be willing to give up in order to consume one more book (B)?

[Hint: Think of books on the X axis.]


Solutions

Expert Solution

U(B,F) =4 √B√F

Budget line: M= PB.B+PF.F

Where M= income, PB= Price of book , PF= Price of food

Budget line: 750=25B+50F

At optimum : MUB/PB= MUF/PF

MUB=∆U/∆B

MUB= 4√F÷2√B = 2√F÷ √B

MUF= ∆U/∆F

MUF= 4√B÷2√F= 2√B÷ √F

So, (2√F÷√B)÷25 = (2√B÷ √F) ÷50

√F ÷ √B= √B÷ 2√F

2F= B

Putting B= 2F in budget line equation

750=25B+50F

750= 50F+50F

F*= 7.5

B= 2F

B*= 15

Answerb)

Optimal bundle = Book,Food= 15, 7.5

750= 25B+50F

If B= 16

750= 25*16 + 50F

F= 7

Earlier she was having 7.5 units of Food and now she is having 7 units of food so , in order to have an additional unit of book she has to give up 0.5 units of food (7.5-7= 0.5)

Rahul Sunny answered 2 years ago
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