Question

Bob consumes food and housing. Suppose his marginal utility from an additional unit of food is 20 and his marginal utility from an additional unit of housing is 100. ​ Furthermore, suppose the price of a unit of food is ​$1.00 and the price of a unit of housing is ​$2.00. Can Bob increase his utility without changing his total expenditures on food and​ housing? Holding expenditures​ constant,
A. Bob can increase utility by spending more on food and the same amount on housing.
B. Bob cannot increase his utility
C. Bob can increase utility by spending more on food and less on housing.
D. Bob can increase utility by spending more on food and more on housing.
E. Bob can increase utility by spending less on food and more on housing.

Answer 1

Answer:

Option (E) is correct.

Explanation:

For utility maximization,

Bob's consumption of Housing and food should be such that:

$\frac{Marginal\ utility\ of\ housing}{Price\ of\ housing}=\frac{Marginal\ utility\ of\ food}{Price\ of\ food}$

Here,

$\frac{Marginal\ utility\ of\ housing}{Price\ of\ housing}=\frac{100}{2}$

                                                                                              = 50

$\frac{Marginal\ utility\ of\ food}{Price\ of\ food}=\frac{20}{1}$

                                                                                   =20

Bob is not maximizing utility, as these two terms are not equal(50 > 20).

Since the marginal utility per rupee spent on housing is greater than that on food.

Hence, Bob can increase his utility just by consuming more of housing and less of food.