Changing the Interest Rate: Savers and Borrowers

I look at what happens when we change the interest rate for savers and borrowers in our two-period intertemporal choice model. We show this graphically.

We look at the consequence of increasing the interest rate on consumption in periods one and two. This changes between borrowers and savers. We also note the diagram for the aggregate economy.

In the previous video, I derive the intertemporal budget constraint for a two-period model of intertemporal choice. I shall derive this for more periods. Check out the playlist for intertemporal macroeconomics as a whole, linked at the end of this video.

We discuss the assumptions of the two-period model of intertemporal choice. This involves consumers living for 2 periods. They can consume, save or borrow in these time periods, allowing for consumption that differs from their income in that period. In order to defer income to other periods, they can buy or sell one-period bonds with interest r.

We can then mathematically write the budget constraint for each of these periods. With a bit of substitution and rearranging, this gives us the intertemporal budget constraint. This says that the present value of consumption is equal to the present value of income. The consumer can thus not spend more than she earns, but will spend all of her income since more consumption is always assumed to increase her utility.

In future videos we shall look at borrowers and savers in more detail, examining what happens with a change (increase or decrease) in the interest rate, changes in income and other exogenous changes.

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