Question

As the interest rate rises, does the intertemporal budget constraint become steeper or flatter?

Short answer

The intertemporal budget constraint becomes steeper.

Step-by-step solution

Understanding the Intertemporal Budget Constraint

The intertemporal budget constraint represents the trade-off between consumption today and consumption in the future. It shows the maximum combination of goods that a consumer can purchase given their income in two different periods.

Analyzing the Impact of Interest Rate on Consumption Trade-off

As the interest rate rises, the return on savings increases, making future consumption comparatively cheaper than present consumption. This affects the slope of the intertemporal budget constraint.

Identifying the Slope Change

The slope of the intertemporal budget constraint is determined by \[ -(1+r) \]where \(r\) is the interest rate. An increase in \(r\) increases \(1+r\), thus making the absolute value of the slope steeper.

Conclusion on the Constraint Slope

When the interest rate rises, the constraint becomes steeper, as future consumption becomes more attractive compared to current consumption.

Key concepts

Interest Rate

The interest rate plays a crucial role in how consumers plan their spending in the present versus the future. When you earn or pay interest on money saved or borrowed, this interest rate dictates the return or cost over time. A higher interest rate means that:

• The cost of borrowing money increases, resulting in less incentive to spend now.
• The return on saving money also rises, encouraging more savings for future use.

Therefore, if you save more due to higher interest rates, you might choose to consume relatively less today to take advantage of these returns in the future.

Consumption Trade-off

The consumption trade-off explains how consumers decide between spending now and spending later. This decision is heavily influenced by the interest rate.
A rise in the interest rate enhances the appeal of saving rather than consuming today. Future consumption becomes more attractive because money saved now grows faster due to increased interest.
However, this trade-off also means that current consumption decreases because consumers prefer to save more. They buy less today to benefit from the higher gains they will receive from saving.

Slope of Budget Constraint

The slope of the intertemporal budget constraint represents how present consumption is traded off for future consumption. It is influenced directly by the interest rate and is defined mathematically as \[-(1+r)\]where \(r\) is the interest rate.
When the interest rate \(r\) increases, so does \((1+r)\), causing the absolute value of the slope to increase. This makes the budget line steeper.
A steeper slope indicates that future consumption is more favorable compared to present consumption, as the relative cost of not consuming now is offset by higher future returns.