Question

Part A

Product X has the following demand and supply functions:

                                    Qd = 30 – 2p

                                    Qs = -10 + 6p

The government does not currently place indirect taxes on Product X. The production and consumption of Product X, however, is considered to be undesirable. The government subsequently places an indirect tax on the product which creates a producers price of $4. Product X also has a coefficient of income elasticity of +2

Use the above information to :

1. Draw a demand and supply graph illustrating the market for Product X both before and after the imposition of the indirect tax.

2. Calculate the tax per unit and total tax collected by the government.

3. Calculate and explain consumer surplus, producer surplus and deadweight loss before and after the imposition of the indirect tax.

4. Calculate the price elasticity of demand for Product X (use the arc method to calculate elasticity)

5. Calculate and explain the burden of the tax. Discuss the relationship between the burden of the tax and the coefficient of elasticity calculated in part iv

Part B

1. The government increases direct (income) tax by 10% and this decreases average disposable income by 3%. Use the above demand and supply functions as a guide to discuss the impact of this policy on the demand for Product X.

2. Explain whether the government is likely to reduce indirect taxes or increase direct taxes in order to discourage the consumption of Product X.

Answer 1

PART A

i) Q*= 20

Quantity after tax goes down to 14

ii) tax per unit and total tax

Per unit tax is $1

Total Tax= Tax amt * new quantity

=1 * 14= $14

iii)

iv) % change in qty / % change in price

% change in qty= (20-14)/((20+14)/2)*100= 35.3

% change in price= ((5-4)/((5+4)/2))*100=22.2

Price elasticity of demand= 35.3/22.2= 1,6