A. [25 points] Suppose the market for cigarettes is characterized by the followi

Question

A. [25 points] Suppose the market for cigarettes is characterized by the following information: Qd=70–5P [Demand] Qs=3P–10 [Supply]

[Note: P = price per unit; Qd = thousands of units demanded; Qs = thousands of units supplied] Suppose the government imposes a sales tax of $2 per unit. Answer questions (i) through (v) below:

i) Calculate the magnitude of the consumer surplus and producer surplus in the pre-tax equilibrium.

ii) Calculate the tax revenue in the post-tax equilibrium.

iii) Calculate the change in consumer surplus due to the sales tax.

iv) Calculatethechangeinproducersurplusduetothesalestax.

v) Calculate the Dead-Weight-Loss due to the sales tax.

B. [25 points] Suppose the government imposes a price ceiling of $50 on a market characterized by the following information:

Qd = 700 - 2P Qs = 100 + 4P
[Note: P = price per unit; Qd = hundreds of units demanded; Qs = hundreds of units supplied]

Calculate the magnitude of deadweight loss from the price ceiling. Find a price floor that will result in the same magnitude of deadweight loss.

Explanation / Answer

A) 1) Pre tax situation

In equilibrium QD = QS

70 - 5P = 3P - 10

At equilibrium P = 10.Equilibrium Q = 70 - 5 * 10 = 20.

Pre tax consumer surplus = 1/2 * 20 * (14 - 10)

1/2 * 20 * 4 = 40.

Pre tax producer surplus = 1/2 * 20 * (10 - 10/3)

1/2 * 20 * 20/3

200/3 = 66.67

After tax situation

At equilibrium QS = QD

New price paid by buyers P + x

New price recieved by sellers P - (2 - x) = P - 2 + x (buyers and sellers together bear tax , buyers bear it by x , sellers by 2 - x as amount of sales tax = 2).

Therefore 70 - 5(P + x) = 3(P - 2 + x) - 10

70 - 5P - 5x = 3P - 6 + 3x - 10

Substituting P = 10 and solving we get x = 0.75.Thus buyers pay price = 10 + .75 = 10.75

Thus sellers bear the tax burden of 2 - 0.75 = 1.25.Thus price recieved by sellers = 10 - 1.25 = 8.75.

2) New quantity can be obtained by substituting value of x in demand curve , we get

70 - 5(P + x) = 70 - 5(10.75) = 16.25

Tax revenue = 2 * 16.25 = 32.50

3) New consumer surplus = 1/2 * 16.25 * (14 - 10.75) = 26.41.Change in consumer surplus 40 - 26.41 = 13.59.

4) New producer surplus = 1/2 * 16.25 * (8.75 - 10/3) = 44.037.Change in producer surplus = 66.67 - 44.037 = 22.635

5) Dead weight loss due to sales tax imposition = 1/2 * 2 * 3.75 = 3.75.

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