In a deflationary recession, lower demand leads to lower prices. Does this contradict the law of demand?

Question

In Principles of Macroeconomics (a free ebook available on openstax), the chapter on inflation says, regarding deflationary recessions:

High levels of unemployment typically accompany recessions, and the total demand for goods falls, pulling the price level down.

So, a lower quantity of a product demanded leads to a lower price for that product. But the law of demand says that a lower quantity of a product demanded leads to a higher price for that product.

It appears to me as if this is a contradiction.

Perhaps I am misunderstanding what “lower quantity of a product demanded” means. Perhaps this means that the demand curve is shifting to the left and hence lowering the competitive price (the price reached at market equilibrium).

Answer 1

No it does not. First you are misrepresenting law of demand. The law of demand states the following (see Mankiw Principles of Economics pp 1; emphasis mine):

Law of demand: Other things being equal, when the price of a good rises, the quantity demanded of the good falls, and when the price falls, the quantity demanded rises.

Note several things:

1. The law of demand states what happens to demand when price changes, it says nothing of how demand changes price.
2. The law of demand holds, as the bold sentence states, all else being equal. In recession when demand falls that is because peoples preference changes and they want to consume less, now all else is no longer equal, there is a change in preference that shifts the demand.

The law of demand simply states that demand should be downward sloping, but downward sloping demand can still shift to the left and right (or some texts use up and down instead of right and left). Shift in demand to the left while holding supply curve constant will result in equilibrium with lower output and prices, but that does not violate the law of demand as demand curve will still be downward sloping and so ceteris paribus when the price of a good rises, the quantity demanded of the good still falls.

Answer 2

Perhaps this means that the demand curve is shifting to the left and hence lowering the competitive price (the price reached at market equilibrium).

Yes.

Indeed the "law" of demand holds only for a given demand function, it does not cover situations where the demand curve shifts; you can come up with two functions $D_1,D_2$ where for some prices $p_1 >p_2$ you have $D_1(p_1) >D_2(p_2)$.