Question

In class, we discussed that if c and c' are normal goods, then the income effect for these two goods will be positive. Now, consider c now is an inferior good, show with 2 separate diagrams, how the optimal c and c' will change if i) there is an increase in lifetime income, and ii) if there is an increase in the interest rate r.

Answer 1

When c is an inferior good, an increase in lifetime income will lead to a decrease in the consumption of c and an increase in the consumption of c'. An increase in the interest rate will decrease the optimal consumption of both c and c'.

Step-by-step explanation:

To show how the optimal consumption of two goods, c and c', will change when c is an inferior good and there is an increase in lifetime income or interest rate, we can create separate diagrams.

1. Increase in lifetime income: When lifetime income increases, the income effect for both normal goods and inferior goods will be positive. However, since c is an inferior good, the increase in income will lead to a decrease in the consumption of c and an increase in the consumption of c'. Therefore, the optimal consumption of c will decrease, while the optimal consumption of c' will increase.
2. Increase in interest rate: An increase in the interest rate will decrease the optimal consumption of both goods, regardless of whether they are normal or inferior goods. This is because a higher interest rate reduces the opportunity cost of saving, making it more attractive than immediate consumption. Therefore, the optimal consumption of both c and c' will decrease.