Question

A consumer has a utility function of U = min{4x1, x2}. The price of good 1 is $8 and the price of good 2 is $5. The consumer has $112 in income. How many units of each good does she consume?

x1 = 8, x2 = 8

x1 = 16, x2 = 4

x1 = 12, x2 = 8

x1 = 4, x2 = 16

None of the above

Consider the inter-temporal model of consumption studied in class, with two possible periods. Consider initially that an individual is a borrower. If the interest rate falls the individual can possibly become a saver?

True

False

If a good is normal, then the law of demand must always hold.

True

False

Answer 1

(1) Option (4)

For a fixed proportion utility function, utility is maximized when 4x1 = x2. Substituting in production function,

112 = 8x1 + 5x2

112 = 8x1 + 5(4x1)

112 = 8x1 + 20x1 = 28x1

x1 = 4

x2 = 4 x 4 = 16

(2) True

When interest rate falls, current consumption becomes less expensive, so the individual will tend to increase current consumption (substitution effect). But lower interest rate will also increase relative income (income effect). For a net borrower, higher relative income increases current consumption, which decreases current saving. So it is possible to become a saver if the increase in current consumption is lower than the increase in real income.

(3) True

For a normal good, both income effect and the negative substitution effect work in same direction, leading to an increase (decrease) in quantity demanded due to a decrease (increase) in price, conforming to the law of demand.