Question

Suppose that the market for cigarettes is a competitive market and is described by the following supply and demand functions:

Demand: QD = 100000 – 500P

Supply: QS= – 20000 + 2000P

Where Q is the number of packets and P is the price per packet of cigarettes.

(a) Calculate the equilibrium price and quantity and draw a diagram to illustrate your answer.

(b) Show on your diagram and calculate the size of the:

(i) Consumer surplus

(ii) Producer surplus

(iii) Total surplus

(iv) Deadweight loss

(c) Suppose the government wants to reduce the consumption of cigarettes to 50000 packets. What size specific (per unit) tax will the government impose on cigarette producers to achieve this outcome?

(d) What is the per unit incidence or burden of the tax experienced byconsumers?

(e) What is the per unit incidence or burden of the tax experienced byproducers?

(f) On a new diagram, show and calculate the size of the following after the introduction of the tax:

(i)Consumer surplus

(ii) Producer surplus

(iii) Tax revenue

(iv) Total surplus

(iv) Deadweight loss

(g) According to the supply and demand model is society worse off or better of as a result of the imposition of the per unit tax? Explain your answer.

Answer 1

(a) Equilibrium price and quantity is where demand = supply
100,000-500P = -20,000+2000P; So, P = 48; Q = 76,000

(b) Consume surplus = ½(200-48)* 76,000 = 5,776,000
Producer surplus = ½*(48-10)*76,000 = 1,444,000
Total surplus = CS+PS = 7,220,000
Deadweight loss = 0

  

(c) $65 per unit.  
reason: as shown in the graph below, to bring down the quantity to 50,000 units, the government has to impose a tax of $65.

(d) Consumers experience a burden of $52 (100- 48 = 52)
(e) Producers experience a burden of $13 (48 - 35 = 13)
(f) Graph:

  

After tax, consumer surplus = ½*(200-100)*50,000 = 2,500,000
Produce surplus = ½*(35-10)*50,000 = 625,000
Total surplus = 3,125,000
Tax revenue = tax amount * quantity after tax = 3,250,000
Deadweight loss = ½*(tax amount)*(lost quantity) = ½*65*(76,000 - 50,000) = 845,000

(g) The society is worse off because there is a deadweight loss of $845,000 caused by tax. This amount reflects the welfare lost by consumers and producers due to decreased quantity after tax.

Total welfare before tax = CS+PS = 7,220,000
Total welfare after tax = CS+PS+Govt revenue = 6,375,000
The difference is deadweight loss = 845,000