Question

The supply and demand functions of a good are given by
P = QS + 8
P = −3QD + 80
where P, QS and QD denote price, quantity supplied and quantity demanded, respectively.
(a) Find the equilibrium price and quantity if the government imposes a fixed tax of
$36 on each good.
(b) Find the corresponding value of the government’s tax revenue.

Answer 1

The computation shows that the equilibrium quantity and price are 20 and 28.

How to calculate equilibrium price?

From the information given,

QS = 8 - P

QD = 26.7 - 0.33P

Equate the quantity demanded and supplied. Therefore,

8 - P = 26.7 - 0.33P

- P + 0.33P = 26.7 - 8

-0.67P = 18.7

P = 18.7/0.67

P = 28

Therefore, the quantity will be:

P = Q + 8

28 = Q + 8

Q = 28 - 8.

Q = 20

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