Steve enjoys pedicures and romance novels Steves marginal ut

Steve enjoys pedicures and romance novels. Steve’s marginal utility for pedicures is given by MU_P = N^0.5/P^0.5 and his marginal utility for novels is given by MU_N = P^0.5/N^0.5, where P is the number of pedicures that Steve receives and N is the number of romance novels he has. Pedicures cost $20 (P_P=20), novels cost $5 (P_N=5) and Steve has a budget of $100. What combination of pedicures and novels will maximize Steve’s utility?

a. 2 pedicures and 12 novels

b. 2.5 pedicures and 10 novels

c. 3 pedicures and 8 novels

d. 4 pedicures and 4 novels

e. none of the above.

Solution

Steve will maximize utility when following condition is fulfilled -

MUP/MUN = PP/PN

(N^0.5/P^0.5)/(P^0.5/N^0.5) = 20/5

N/P = 4

N = 4P

Budget line equation is as follows -

(Price of pedicure * number of pedicures) + (Price of novels * number of novels) = Total income

(PP * P) + (PN * N) = $100

20P + 5N = 100

20P + 5(4P) = 100

20P + 20P = 100

40P = 100

P = 100/40 = 2.5

N = 4P = 4*2.5 = 10

Thus,

Steve\'s utility will be maximized when he consumes 2.5 pedicures and 10 novels.

Hence, the correct answer is the option (b).