# EFFICIENCY AND INCIDENCE

Suppose the NJ government decides to impose a $1,000 per student tax on colleges--each college has to pay $1,000 for each student enrolled. The supply curve of college education (before tax) is Qs = 40P, and the demand curve is Qd = 400,000 - 10P.

a. Find the pre-tax equilibrium price and quantity.

b. Find the equilibrium price after the tax is imposed. What are the quantity, price paid by consumers, and price recieved by sellers?

c. Find the government tax revenue and approximate the excess burden caused by the tax. Why is your measure of excess burden an approximation (what information are you missing)?

d. What would have happened (how would your answers to a,b,c change if the tax were paid by students instead of colleges?

e. Repeat (b) assuming that the supply of education is given by Qs = 320,000. How does the incidence of the tax compare with the incidence in part (b)? How does the excess burden compare? How does the government revenue compare?

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#### Solution Preview

a. Find the pre-tax equilibrium price and quantity.

<br>We have

<br>Q=40p

<br>Q=400000-10p

<br>Then at the equilibrium, 40p=400000-10p

<br>Or p=8000

<br>Then Q=40*8000=320,000

<br>

<br>b. Find the equilibrium price after the tax is imposed. What are the quantity, price paid by consumers, and price received by sellers?

<br>

<br>for the supplier, the tax is like a decrease in their unit price,

<br>so the new supply is Q=40(p-1000)

<br>the demand is unchanged: Q=400000-10p

<br>then 40(p-1000) =400000-10p

<br>or p'=8800

<br>then Q'=40(8800-1000)=312,000

<br>which means that students pay 8800, but the colleges have to pay 1000 for tax and ...

#### Solution Summary

Find the equilibrium price after the tax is imposed