The relative price of second-period consumption in terms of first-period consumption is ____.
The correct answer and explanation is:
The relative price of second-period consumption in terms of first-period consumption is (1 + r), where r is the real interest rate.
Explanation:
In economics, when considering consumption over two periods — typically called period 1 (present) and period 2 (future) — the relative price of consumption in the second period relative to the first period is a fundamental concept. This concept reflects how much first-period consumption you must give up to consume one more unit in the second period.
- Intertemporal Choice and Interest Rate: When you consume in the future (second period), you forego the chance to consume today (first period). Conversely, by saving today (not consuming all your income), you can invest your savings and earn interest. The interest rate r measures the return on saving or the cost of borrowing.
- Relative Price: The relative price of second-period consumption (future consumption) in terms of first-period consumption (present consumption) is given by: Relative price=1+r\text{Relative price} = 1 + r This means that one unit of second-period consumption costs 1 + r units of first-period consumption.
- Why is it 1+r1 + r?
- If you save one unit of consumption today, you will have 1+r1 + r units in the next period.
- To consume one unit in the second period, you must have saved 11+r\frac{1}{1 + r} units today.
- Therefore, from the perspective of first-period consumption, second-period consumption is more expensive by the factor 1+r1 + r.
- Implications:
- A higher interest rate rr increases the relative price of future consumption. This means future consumption is more “expensive” in terms of present consumption, incentivizing people to consume more now and less later.
- A lower interest rate makes future consumption cheaper relative to present consumption, encouraging saving.
- Example: If the real interest rate is 5% (i.e., r=0.05r = 0.05), then the relative price of second-period consumption is: 1+0.05=1.051 + 0.05 = 1.05 So, consuming 1 unit next period costs you 1.05 units today, reflecting the opportunity cost of consuming later.
In summary, the relative price of second-period consumption in terms of first-period consumption is 1 + r, reflecting the trade-off between consuming now and consuming later given the interest rate. This relationship is central to models of intertemporal consumption choice and saving behavior in economics.