An individual is concerned about her consumption in two periods 0 and 1. In period 0 her income will be $83,000 and in period 1 it will be $40,000. She would like to have exactly 3 units of consumption in 0 for every 2 units of consumption in 1. She can borrow or save at interest rate of 25% . How much does she borrow or save in 0?

To solve this problem, we need to balance the individual's consumption and savings/borrowing across two periods (period 0 and period 1), given the income and interest rate. Here's how we can break it down step by step:

### 1. **Define Variables:**
- Let $ C_0 $ be the consumption in period 0.
- Let $ C_1 $ be the consumption in period 1.
- Income in period 0 = $83,000.
- Income in period 1 = $40,000.
- Interest rate $ r = 25\% = 0.25 $.
- The condition on consumption is that she wants $ \frac{C_0}{C_1} = \frac{3}{2} $, or equivalently, $ C_0 = 1.5 C_1 $.

### 2. **Budget Constraint:**
Since she can borrow or save at a 25% interest rate, her consumption in the two periods is related by the present value of her income. The total present value of consumption over both periods must equal the total present value of her income:

\[
C_0 + \frac{C_1}{1 + r} = \text{Income in period 0} + \frac{\text{Income in period 1}}{1 + r}
\]

Substituting the values:

\[
C_0 + \frac{C_1}{1.25} = 83,000 + \frac{40,000}{1.25}
\]

\[
C_0 + 0.8C_1 = 83,000 + 32,000
\]

\[
C_0 + 0.8C_1 = 115,000
\]

### 3. **Substitute Consumption Condition:**
From the consumption preference, $ C_0 = 1.5 C_1 $. Substituting this into the budget equation:

\[
1.5 C_1 + 0.8 C_1 = 115,000
\]

\[
2.3 C_1 = 115,000
\]

Solving for $ C_1 $:

\[
C_1 = \frac{115,000}{2.3} = 50,000
\]

### 4. **Calculate $ C_0 $:**
Now that we know $ C_1 = 50,000 $, we can find $ C_0 $:

\[
C_0 = 1.5 \times 50,000 = 75,000
\]

### 5. **Determine Borrowing or Saving:**
- In period 0, her income is $83,000, and her consumption is $75,000. Since her income exceeds her consumption, she will save the difference:

\[
\text{Savings in period 0} = 83,000 - 75,000 = 8,000
\]

Thus, she will **save $8,000** in period 0.

### Final Answer:
The individual will save $8,000 in period 0.

---

Do you need further details or have any other questions?

### Follow-up Questions:
1. How would the solution change if the interest rate were different?
2. What if the consumption preference was reversed (i.e., 2 units in period 0 for 3 units in period 1)?
3. How much will she have saved by period 1 after accounting for interest?
4. What happens if her period 1 income increases or decreases significantly?
5. How does borrowing affect her future consumption in this scenario?

### Tip:
When solving intertemporal consumption problems, always check whether the interest rate allows for borrowing or saving to maximize utility over time.

An individual is concerned about her consumption in two periods 0 and 1. In period 0 her income will be $83,000 and in period 1 it will be $40,000. She would like to have exactly 3 units of consumption in 0 for every 2 units of consumption in 1. She can borrow or save at an interest rate of 25%. How much does she borrow or save in 0?

Learn how to solve an intertemporal consumption problem involving two periods, given income levels and an interest rate. This problem explains how to calculate borrowing or saving using key economic concepts like budget constraints and present value. Suitable for undergraduate students in economics or finance.

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