Is there such a thing as a supply shortage?

See The Art Market Hits a Wall: Christie’s sold $3.2 billion in art during the first half of 2023, a 23% drop from the year before as sellers held onto more of their art trophies by Kelly Crow of The WSJ. Excerpts:

The article talks about art galleries and auction houses seeing a decline in revenue. But I can't tell if that is from selling fewer paintings or the price falling. One expert "blamed a supply shortage for the drop in its overall sales during the first half of the year."

I don't think there is such a thing as a supply shortage. Supply is the relationship that price and quantity have with each other. A shortage is when the quantity demanded is greater than the quantity supplied and the current price is below where supply and demand intersect.

Maybe the expert meant to say that the supply curve or line shifted to the left (a decrease in supply), as the article title implies. Then price would rise and quantity would fall. Revenue could go up or down, depending upon the price elasticity of demand. Since it fell, it implies the demand is elastic. More on this relationship below.

There could be a shortage temporarily. But the price would have to rise eventually to get back to equilibrium. The article never says anything about the average price of art going up.

Demand could have fallen or shifted to the left. Then both P and Q fall, so that revenue definitely falls. But I would not call this a "supply shortage." It just means that the quantity supplied decreased since we move along the supply line. We move to a new equilibrium and at no time is there a shortage (again, a shortage is when the quantity demanded is greater than the quantity supplied and the current price is below where supply and demand intersect). Maybe there was a temporary surplus until price falls. But no shortage.

This statement from the article suggests a fall in demand: 

"Sales at Christie’s and Sotheby’s slowed dramatically this spring as seasoned collectors chose not to ply their art troves into an uncertain economy." 

If that is the case, then we are just back to a fall in quantity supplied and no shift in supply.

Price elasticity of demand-It tells us how responsive quantity demanded (Q_d) is to a change in price. That is, when price changes, will the change in Q_d be large or small? The bigger the change in Q_d  the greater will be the price elasticity of demand.

We will use E_d to stand for price elasticity of demand. Here is the definition 

E_d = % change in Q_d /% change in P 

E_d = %DQ_d /%DP

where D (the Greek letter delta) means "change in."

OR  E_d = % change in Q_d divided by % change in P.

This table shows the relationship that E_d has with total revenue (what happens to TR when P changes in different cases of E_d). If P falls and E_d is less than one, TR falls.

Ep	Price	TR
> 1	Increase	Decrease
> 1	Decrease	Increase
= 1	Increase	No change
= 1	Decrease	No change
< 1	Increase	Increase
< 1	Decrease	Decrease

Another way to see the relationship between price changes and changes in TR is to look at the price elasticity of demand and changes in TR.

If   E_d = % change in Q_d /% change in P  = 10/5 then  E_p  > 1

            

Now look at TR = P*Q. If P goes down 5% it would lower TR. But, since Q goes up 10%, if more than offsets the fall in Q and TR will rise. Notice in the table that if E_d  > 1, a decrease in price means an increase in TR. And an increase in price means a fall in total revenue (this was mentioned above).