Question

1. Eric consumes only books and wine. His utility function is given by: U (B,W)= B^.5W^.5

Each unit of book costs him $12 and the price of a bottle of wine is $15. His income is $240.

• (I) Write the equation of Eric’s budget constraint.DRAW his budget constraint with books on the vertical axis and wine on the horizontal axis.
• (II) What is Eric’s total spending on books when he maximizing utility?
• (III) Find the utility maximizing choice of bundle?
• (IV) What is the maximum utility that Eric can receive?

Answer 1

U= B^0.5 W^0.5

(a) Budget constraint = P_b B + Pw W = I

12 B + 15 W = 240

When W =0, B= 20

When B= 0, W= 16

By plotting this we get the budget constraint.

(b) At utility maximization bundle MRS= MUw/MUb = Pw/Pb

(0.5B^0.5 W^-0.5)/ (0.5B^-0.5 W^0.5)= (15/12)

B/W = 5/4

B = 5W/4

Now, put this into the budget constraint ,we get :

12 (5W/4) + 15W = 240

15 W + 15W = 240

30W= 240

W = 8 units

B= 5W/4 = 5(8)/4 = 10 units

So, total spending on books when he maximizing utility is (12)(10)= $120.

(c) The utility maximizing bundle is (8 wine , 10 books).

(d) The maximum utility that Eric can receive , U= 10^0.5 8^0.5 = (3.16)(2.82)= 8.93