Question

Brendan’s utility function is 1 2 1 2 u(x , x ) = x x . The prices of 1x and 2 x are $2

and $2 respectively. Brendan has an income of $20.

(i) How many of each good will he consume to maximize his total utility?

(ii) What the maximum utility level does he receive? (Hint: For the utility

function 1 2 1 2 u(x , x ) = x x , you have the 1 2 MU = x and 2 1 MU = x ).

(iii) Suppose that Brendan’s income increases to $32 but a tax is placed on

1 x so that 1 x costs Brendan $4 each while the price of 2 x stay the same,

how many 1 x and 2 x will he consume now? What the maximum utility

level will he receive in this case?

Answer 1