Question

Maria’s preference over milk-shakes and fruit-smoothies is described by the utility function u(M, F) = M^3/4 + 3F, where M is the amount of milk-shakes and F the amount of fruit-smoothies she consumes every week. The price of milk-shakes is $4, and fruit-smoothies cost $8 per unit. Which of the following is true about Maria’s weekly consumption when she spends $16 every week on shakes and smoothies? (Assume that both goods are perfectly divisible)

a. Maria is consuming more fruit-smoothies than milk shakes

b. Maria would consume more milk shakes if she had more money to spend on the two goods.

c. Maria would consume less smoothies if their price increased to $9 per unit.

d. more than one of the above (false) e. none of the above

Answer 1

From the utility function the marginal rate of substitution is given by MRS = -MUM/MUF = -0.75M^-0.25/3 or -0.25M^-0.25

Slope of the budget line is given by the price ratio which is -4/8 or -0.5

at the optimal choice the marginal rate of substitution is equal to the slope of the budget line. This implies -0.25M^-0.25 = -0.5 or M= 1/16. This also gives the quantity of fruit smoothies = (16 - 4*1/16)/8 = 1.96.

The quantity of milk shakes is fixed and it is irrespective of the income which means option B and option C are incorrect.

Therefore select option A.