The market for packets of cigarettes has been described by the following supply

Question

The market for packets of cigarettes has been described by the following supply and demand functions:

Supply: P = 10 + 4Q Demand: P = 100 – 5Q where P is the price in dollars and Q is the quantity of packets of cigarettes per month (in thousands).

PART A) Construct a graph of supply and demand for this market showing all intercepts. What are the equilibrium prices and quantities? Show these on your graph.

Part B) At the market equilibrium price, what would be the total monthly revenue?

PART C) Calculate consumer surplus at the market equilibrium and indicate this surplus as an area on your diagram.

PART D) Calculate producer surplus at the market equilibrium and indicate this surplus as an area on your diagram.

PART E) Assume that a per-unit tax of $9.00 per packet of cigarettes is imposed by the government on the suppliers of cigarettes. Depict this on your demand and supply diagram. (Hint: the new tax inclusive supply function will be: P = 19 + 4Q). What is the new market equilibrium quantity? What price will consumers now pay and what price will suppliers now receive?

PART F) How much is the government revenue from the tax on suppliers?

PART G) Calculate consumer surplus and producer surplus after the imposition of the tax and any deadweight loss associated with the tax. Indicate these surplus and tax revenue areas on your diagram. Explain what the deadweight loss represents.

PART H) Now assume that instead of imposing a per-unit tax of $9.00 per pack on the suppliers of cigarettes the government decides to apply the same per-unit tax of $9.00 on consumers. Depict this on your demand and supply diagram. (Hint: the new tax inclusive demand function will be: P = 91 – 5Q) What is the new market equilibrium quantity? What price will consumers now pay and what price will suppliers now receive? (5 marks)

PART I) How much is the government revenue from the tax on consumers? (1 mark)

PART J) Who bears the greatest burden of the tax in each case, producers or consumers? Does your answer depend on whether the tax is levied on producers or consumers?

I am really having difficulty understanding Part J- can that please be answered with some detail?

Explanation / Answer

PART - J (As mentioned)

Demand: P = 100 - 5Q [Q = (100 - P) / 5 = 20 - 0.2P]

Supply: P = 10 + 4Q [Q = (P - 10) / 4 = 0.25P - 2.5]

In equilibrium, demand price = Supply price

100 - 5Q = 10 + 4Q

9Q = 90

Q = 10

P = 10 + (4 x 10) = 10 + 40 = 50

Price elasticity of demand = [dQ/ dP(demand)] x (P / Q)

= - 0.2 x (50 / 10) = - 1

Price elasticity of supply = [dQ/ dP(Supply)] x (P / Q)

= 0.25 x (50 / 10) = 1.25

So, absolute value of elasticity of demand is less than absolute value of elasticity of supply. This means that Demand is more inelastic than supply.

When demand is more inelastic, for any type of tax imposed, producers bear more tax burden than consumers. This result does not depend on whether tax is levied on consumers or on producers.

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