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Intertemporal choice

Income now versus later

An individual’s consumption is affected by the timing of their income flows. Let’s examine two scenarios with a 10% interest rate and $110 of income.

Option 1

You get $110 now but nothing in the future.

If you choose to spend all of your money now, then your consumption is $110 now and $0 in the future.

If you choose to save all your money, then your consumption is $0 now and $121 in the future. Since you kept the money you earned in the bank, you gained 10% more because of interest.

\[110 \times 1.10 = 121\]

Option 2

You get nothing now but $110 in the future.

If you have only future income, with no current income, you must borrow in order to consume. Remember this equation:

\[\text{repayment} = \text{principal} + \text{interest}\]

The most that you could consume now while still being able to settle your debt in the future is $100. This is because $100 × 10% interest rate = $10 of interest. Repayment is interest plus principal, so if you borrow $100 you repay $110 in the future (since $100 + $10 is $110). You cannot borrow more than $100 because you will have to repay more money than is possible with your future income.

On the other hand, if you choose to spend in the future, then you consume $0 now and $110 in the future. You don’t earn interest on this future income since you aren’t keeping the money in the bank or lending it to others while you wait to consume it.

Note that you can only borrow what you are able to repay (factoring in interest). This means that there are limits on how much you can borrow in the present. This is where the intertemporal budget constraint comes into play.

Building your own budget constraint

What is a budget constraint? A budget constraint represents the combinations of immediate and future consumption that are available to you given a fixed income and interest rate. The \(x\)-axis is how much you are able to consume now given your current and future incomes. The \(y\)-axis is how much you are able to consume later given your current and future incomes. Let’s use this information build a budget constraint.

Step one: Viewing the endowment point

Borrowing and lending allow us to rearrange our capacity to buy goods and services across time. In a scenario where we are not able to lend or borrow our money, our endowment dictates how much we can spend in current and future periods. Thus, the first step in building our budget constraint graph is plotting the endowment point. This refers to an initial allocation of resources that an individual possesses without any borrowing or lending involved. It can be based on current income or future income. Try moving the sliders below to adjust the position of the endowment point.

Endowment point visualization

Step two: Incorporating the interest rate

The second step in building a budget constraint is factoring in the interest rate. Observe how the budget constraint (blue line) shifts as you adjust the slider to change the interest rate.

Budget constraint with interest rate

Explore real-world interest rates by hovering over countries on this map.

Exercise

Suppose you have a current income of $50 and a future income of $100. If the interest rate for borrowing and lending is 20%, what is the maximum amount that you can consume in the future (i.e. \(y\)-intercept of your budget constraint)?

  • $170
  • $160
  • $100
  • $150
  • If interest rate is 20%, you can lend or save up to $60 \((\$50 \times 1.2 = \$60)\). Thus, your maximum future consumption will be income earned in the future ($100) + income earned now with interest ($60) = $160.
  • If interest rate is 20%, you can lend or save up to $60 \((\$50 \times 1.2 = \$60)\). Thus, your maximum future consumption will be income earned in the future ($100) + income earned now with interest ($60) = $160.
  • If interest rate is 20%, you can lend or save up to $60 \((\$50 \times 1.2 = \$60)\). Thus, your maximum future consumption will be income earned in the future ($100) + income earned now with interest ($60) = $160.

Exercise

Now, assume that interest rate increases to 68%. As a result, the budget constraint will become:

  • Steeper
  • Flatter
  • Stay the same
  • If interest rate increases, the budget constraint will become steeper. Try adjusting the slope in the interactive graph above to observe this change.
  • If interest rate increases, the budget constraint will become steeper. Try adjusting the slope in the interactive graph above to observe this change.