Income and Substitution Effects: Hicks Decomposition

I decompose the change in consumption from a change in the interest rate into income and substitution effects. This is done graphically. The method used is called the Hicks decomposition. We can write the overall change in consumption as the sum of the income and substitution effects. This is called the Slutsky decomposition.

In previous videos, I derive the intertemporal budget constraint for a two-period model of intertemporal choice. I shall derive this for more periods. I later discuss the changes in consumption from a change in the interest rate for a borrower and a saver. 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 in the interest rate, changes in income and other exogenous changes.
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