How would a decrease in expected interest rates over one’s working life affect one’s intertemporal budget constraint? How would it affect one’s consumption/saving decision?

Intertemporal budget constraints indicate the trade-offs individuals face between consuming goods in the present and consuming in the future. It is a concept used in economics to understand how people make decisions about how much they should consume and save based on their income and preferences over their lifetimes. The intertemporal budget constraint can be represented by the following equation: \[C_1 + \frac{C_2}{1+r} = Y_1 + \frac{Y_2}{1+r}\] Where: \(C_1\) = consumption in period 1 (present); \(C_2\) = consumption in period 2 (future); \(Y_1\) = income in period 1; \(Y_2\) = income in period 2; \(r\) = the real interest rate.

The real interest rate (r) is the rate of return on savings. In the context of the intertemporal budget constraint, a higher interest rate means a higher return on savings, which can lead people to save more in the present and consume more in the future. Conversely, a lower interest rate means a lower return on savings, which can lead people to save less in the present and consume more now.

A decrease in expected interest rates affects the intertemporal budget constraint equation, by lowering the value of `r`. As a result, the term \(\frac{C_2}{1+r}\) will increase, indicating that the present value of future consumption increases. Likewise, the term \(\frac{Y_2}{1+r}\) will also increase, meaning the present value of future income increases as well. Graphically, this can be represented by a flattening of the intertemporal budget constraint line, as the decrease in interest rates implies an increase in the relative value of future consumption.

A decrease in expected interest rates will affect an individual's consumption and savings decisions. With a lower interest rate, the return on savings is reduced, causing the following behavior: 1. People are likely to save less, as the reward for saving is decreased. 2. People are more likely to consume more in the present, as the cost of borrowing (or the opportunity cost of consuming more in the future) is lower. 3. The reaction on people's consumption patterns will depend on their preferences between current and future consumption. People with a stronger preference for present consumption will likely consume more now, while others may not change their consumption as much. In summary, a decrease in expected interest rates over one's working life will affect the intertemporal budget constraint by increasing the present value of future consumption and income. This change in the constraint can lead to people saving less and consuming more in the present, depending on their preferences for current and future consumption.