Question

There is market for diamonds. The demand for diamonds per milligram is determined by QD = 40 - 0.4P while its supply is determined by QS = 0.1P.

Suppose a tax of $20 per milligram od diamonds is imposed on the consumers of diamonds.

(a) What is the equilibrium market price and the equilibrium quantity in the market for diamonds prior to the introduction of the tax? What is the equilibrium market price and quantity after the tax is introduced?

Remember that P is the market price per unit: be careful in rearranging the demand function and in correctly incorporating the tax into it.

(b) Now draw a diagram with the demand and supply curves, both before and after the tax was introduced. Label each curve and axis, the old and new equilibrium prices and quantities, and the consumer and producer prices with the tax. You have seen this kind of diagram on the textbook and in the lectures.

(c) How much tax burden falls on consumers? and on producers? Write these down both in levels (i.e. in dollars) and as a proportion (i.e. %).

(d) Calculate the amount of government revenue collected and the amount of deadweight loss, and outline and label these areas in your diagram

Answer 1

a) Q = 40 - 0.4P

0.4P = 40 - Q

P = 100 - 2.5Q                 [This is inverse demand function]

Q = 0.1P

P = 10Q                           [This is inverse supply function]

At equilibrium,

Demand = Supply

100 - 2.5Q = 10Q

12.5Q = 100

Q = 100 / 12.5 = 8

P = 10Q = 10(8) = $80

Thus, prior to the introduction of the tax, the equilibrium market price is $80 per miligramand the equilibrium quantity is 8 miligram.

When a tax of $20 per miligram is imposed on consumers of diamonds, the consumer will pay P + 20. Thus, the new demand function becomes,

P + 20 = 100 - 2.5Q

P = 80 - 2.5Q

The new equilibrium is,

80 - 2.5Q = 10Q

12.5Q = 80

Q = 80 / 12.5 = 6.4

P = 10Q = 10(6.4) = $64

Substituting the value of Q = 6.4 in the initial demand function,

P = 100 - 2.5Q = 100 - 2.5(6.4) = $84

Thus, after the introduction of the tax, the equilibrium market price is $64 per miligramand the equilibrium quantity is 6.4 miligram.

b)

After tax, the consumer pays $84 and the producer receives $64 per miligram.

c) The tax burden on consumer = 84 - 80 = $4

The percentage of tax burden on consumer = (4 / 20) * 100 = 20%

The tax burden on producer = 80 - 64 = $16

The percentage of tax burden on producer = (16 / 20) * 100 = 80%

d) Government revenue = $20 * 6.4 = $128

DWL = 0.5[(84 - 64) * (8 - 6.4)] = $16