Suppose the Government Imposes a Tax of $6 Per Unit

question 20

Essay

Suppose the government imposes a tax of $6 per unit of Good A.What is the incidence of this tax on consumers and producers?
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 $6.We find the tax equilibrium output by setting P_C = P_P + 6:
80 - ½ Q = 14 + Q + 6
Q = 60/1.5 = 40
Now consumers pay P_C = $60 and producers pay P_P = $54 (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 20 and width 40 which equals $400.Producer surplus is now equal to the area of a triangle with height 40 and width 40 which is $800.The tax affects consumers by increasing the price they pay from $58 to $60 resulting in a loss of consumer surplus of $84.The tax affects producers by decreasing the price they receive from $58 to $54 resulting in a loss of producer surplus of $168.

---

Definitions:

Large-Sample Z

A statistical method used for hypothesis testing and confidence interval estimation, appropriate when the sample size is large, typically using the Z-distribution.

Plus Four Estimate

A technique in statistics, particularly in bootstrap methodology, to produce a more robust estimate by adding four observations - two at each end of the sample data.

Failed Items

Products or components that do not meet the predefined quality criteria, resulting in a failure.

Random Sample

A subset of a population selected in such a way that each member has an equal chance of being chosen.