Ge consumes only blueberries and whipped cream and has utility U=((min{B1,W1})^2

Question

Ge consumes only blueberries and whipped cream and has utility U=((min{B1,W1})^2)*(min{B2 , W2}) where B1=blueberries in the first period, W1= whipped cream in the first period, B2=blueberries in the second period and W2=whipped cream in the second period. Her first period income is $100 and her second period income is $218. She can borrow and lend at 9% interest. The sticker price of all goods in all time periods is one. There is no inflation.

a. Find the optimal blueberries and whipped cream consumed in period one and period 2.

Explanation / Answer

Answer

U=((min{B1,W1})^2)*(min{B2 , W2})

Pw = PB = 1

Lets begin with what we learnt in our 12th maths.

max xy^2

given x+ y = c

then we have x = y

We use same concept in this question

and we have

(min{B1,W1}) = (min{B2,W2})

it means income at both period should be same

Lets assume he will take x amount as loan

and

100 + x = 218 - x - (9/100)x

=> 2x + (9/100)x =118

=> 209x/100 = 118

=> x = 56 (approx)

this means he should borrow $56 in first period

As this is a perfect compliment good case B1 = B2 156/2 = 78

Similarly B2 = W2 = 156/2 = 78

Hence he will consume 156/2 = 78 units each of both Blueberries and whiped cream at both time periods

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