Below are notes on Quota and Allocative Efficiency from elearneconomics.
When the government imposes a quota (a restriction on the quantity that can be produced, exported or imported) it forces the market price up and decreases the quantity sold or produced. Because the market is not allowed to clear (restore or reach the equilibrium) there is a loss of allocative efficiency (termed a deadweight loss). Part of the original consumer surplus and producer surplus is not picked up as part of the quota. Consumer surplus and producer surplus are no longer maximised.
At the original equilibrium (P1, Q1) the value of consumer surplus for butter is $80m (0.5 x 40m x $40, area P3CP1) and the value of producer surplus for butter is $160m (0.5 x 40m x $8, area P1CP0), the market is allocatively efficient because consumer surplus and producer surplus are maximised. When the government imposes a quota and restricts the quantity to 30m (Qs) there is a change in consumer surplus, producer surplus and allocative efficiency.
The total value of consumer surplus decreases by $35m because consumer surplus before the quota was $80m and is now $45m (0.5 x 30m x $3, area P3BP2). The higher price means that the difference between what consumers are willing to pay and what they actually pay will decrease. The lower quantity demanded (30m units rather than 40m units) means there are fewer units from which wool buyers can gain a surplus. Therefore, consumer surplus will decrease.
The total value of producer surplus increases by $20m because producer surplus before the quota was $160m and is now $180m ($9 plus $3 divided by 2 multiplied by 30m area P2BFP0). Producer surplus will increase despite some loss of producer surplus due to the lower quantity sold, 30m (Qs) rather than 40m (Q1). The increase in producer surplus is a result of the higher price from the quota that is more than sufficient to offset the loss of producer surplus due to lower sales. Overall producer surplus increases.
There will be a loss of allocative efficiency because the loss in consumer surplus (CS) of $35m outweighs the gain in producer surplus (PS) of $20m, which results in a net welfare loss (deadweight loss) of $15m (0.5 x 10m x $3, area BCF). This is because producer surplus and consumer surplus are no longer maximised following the imposition of the quota on butter.
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