Question

In the given utility function U(c₁,c₂) where c₁​ is Patience's consumption in period 1 and c₂ is her consumption in period 2, and given that her income in period 1 is three times as large as her income in period 2, at what interest rate will she choose to consume the same amount in period 1 as in period 2?

a. 20%
b. 13%
c. 25%
d. 0%
e. 80%

Answer 1

To find the interest rate at which Patience will choose to consume the same amount in period 1 as in period 2, we need to set up an equation based on her utility function and income levels. By solving this equation, we find that the interest rate is 0%.

Step-by-step explanation:

To find the interest rate at which Patience will choose to consume the same amount in period 1 as in period 2, we need to consider her utility function and income levels in each period. Since her income in period 1 is three times as large as her income in period 2, we can set up the equation:

U(c₁, c₂) = c₁ = c₂

Let's assume that the interest rate is r%. In period 1, her consumption is c₁ = 3c₂. In period 2, her consumption is c₂. Using the utility function, we have:

U(3c₂, c₂) = 3c₂ = c₂

Simplifying the equation, we get:

2c₂ = 0

This equation shows that for Patience to consume the same amount in period 1 as in period 2, the consumption in period 2 should be zero. Therefore, the interest rate at which she will choose to consume the same amount in both periods is 0% (option d).