The shortage under a price ceiling

In this video, we calculate the shortage caused by a price ceiling.

Question one. Demand is Q d equals one hundred minus two P and supply Q s equals two P minus twenty. A price ceiling of twenty-five rupees is set: find the shortage.

First, put quantity on the horizontal axis and price in rupees on the vertical axis. Draw demand, D, sloping down, and supply, S, sloping up. At equilibrium, quantity demanded equals quantity supplied, so one hundred minus two P equals two P minus twenty.

This gives four P equals one hundred and twenty, so the equilibrium price is thirty rupees.

Substituting thirty gives equilibrium quantity forty units; mark their intersection E.

Now draw the ceiling at twenty-five rupees, below equilibrium, so it is binding. At this price, quantity supplied is two times twenty-five minus twenty, which equals thirty units.

Mark the supply point at quantity thirty and price twenty-five. Quantity demanded is one hundred minus two times twenty-five, which equals fifty units.

Mark the demand point at quantity fifty and price twenty-five. Shortage equals quantity demanded minus quantity supplied.

So fifty minus thirty gives a shortage of twenty units.

Check: the binding ceiling makes buyers demand more than sellers supply. Hence, the shortage is twenty units.