Initially, P0 and Q0 are the equilibrium price and quantity (i.e. the price and output that would prevail without government regulation. However, the government decides that P0 is too high and has mandated that the price cannot be higher than a maximum ceiling price, which is denoted by Pmax.
Because the price is lower, producer (particularly those with higher costs) will produce less and supply will be Q1. Consumers will demand more at this low price and would like to purchase Q2 and a shortage or excess demand develops which is Q2 - Q1.
Application of Consumer and Producer Surplus. Price controls.
With price control the price would be at Pmax. Some consumers would be rationed out of the market because of the price controls, and production and sales would fall down from Q0 to Q1. Those consumers who can still purchase the good now can do so at a lower price and thus enjoy an increase in the consumer surplus shown in rectangle A. However, some consumers can no longer buy the good, their loss of consumer surplus is given by triangle B, the net change in consumer surplus is therefore A - B, following an imposition of price control also linked to that rectangle A is greater than triangle B, so net change in consumer surplus is positive.
Producer surplus.
Those producers who are still in the market and producing Q1 are receiving a lower price Pmax and have lost producer surplus of an amount given by the rectangle A. However, total production has also dropped and this represents an additional loss in producer surplus and is given by the triangle C.
The total change in producer surplus is (-A - C). Price controls result a net loss of total surplus, which we call a deadweight loss (-B - C)
Total change in total surplus which (A-B) + (-A-C) = -B-C => deadweight loss. This DW loss is inefficiency caused by price controls. The loss of the producer surplus is greater than the gain in consumer surplus.
Change in producer and consumer surplus - the effect of price controls.
Calculate:
Change in consumer surplus,
A - B = ∆ CS.
18 ($1) - 0.5 (2) ($0.40) = $ 17.6 millions
Change in producer surplus.
∆ PS = - A - C = -18 ($1) - 0.5 (2) ($1) = - $19 millions
Total change in surplus. = deadweight loss
DWL=(A-B) + (-A - C) = -B - C = ∆ CS + ∆ PS = $17.6 millions - $19 millions =
– $1.4 millions.
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