Suppose the Government Imposes a Tax of $12 Per Unit

Suppose the government imposes a tax of $12 per unit of Good A.What is the incidence of this tax on consumers and producers?
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In order to answer this question,we need to determine the changes in consumer and producer surplus that result from the imposition of the tax.Without the tax,the competitive equilibrium output can be found by equating demand and supply:
80 - ½ Q = 14 + Q
Q = 66/1.5 = 44
Producers and consumers both pay the same price P = $58.The consumer surplus is equal to the area of a triangle with height 22 and width 44 which is $484.The producer surplus is equal to the area of a triangle with height 44 and width 44 which is equal to $968.With the tax,the consumer price will equal the producer price plus $12.We find the tax equilibrium output by setting P_C = P_P + 12:
80 - ½ Q = 14 + Q + 12
Q = 54/1.5 = 36
Now consumers pay P_C = $62 and producers pay P_P = $50 (notice the difference between the two price levels is equal to the per unit tax).The consumer surplus is now equal to the area of a triangle with height 18 and width 36 which equals $324.Producer surplus is now equal to the area of a triangle with height 36 and width 36 which is $648.The tax affects consumers by increasing the price they pay from $58 to $62 resulting in a loss of consumer surplus of $160.The tax affects producers by decreasing the price they receive from $58 to $50 resulting in a loss of producer surplus of $320.