Problem 1. For commodity X, average cost is equal to marginal cost at every level of output (AC = MC = constant). Draw graphs for part a and b.
a. Assume that the market for X is competitive, analyse the effects when an ad valorem tax of t percent is imposed.
b. Now, analyse the effects of the same tax assuming that the market for X is monopolistic.
c. Briefly discuss the differences in results in part a and b.
Problem 2. Suppose that the demand curve for a particular commodity is QXD = 2000 - 200Px. The supply of commodity X is QXS = 200Px.
a. Find the price and quantity of commodity X assuming the market is competitive.
In an effort to reduce the consumption of good X, the government puts a tax of $2 per unit, collected from the producers.
b. Calculate the quantity of good X consumed after the tax, the price paid by the consumers and the price received by the producers.
c. Calculate government revenue. How much of this revenue comes from consumers and how much from producers?
d. How much quantity is consumed, if the same tax is collected from the consumers? How much is the tax burden on each side.
Suppose the government wants to use an ad valorem tax instead of a unit tax.
e. Calculate the required tax rate, t, such that the quantity stays same as the tax-per-unit quantity in part b.
f. Calculate government revenue.
g. Draw a graph and show the before- and after-tax quantities, supply and demand curves and government revenue. (You can assume tax is collected from the producer.)
Problem 3. Petroleum refining is one of the most capital-intensive industries in Canada. Suppose that we have two industries, the petroleum industry (P) and the non-petroleum industry (NP), and that both industries use labour (L) and capital (K) as factors of production. Use a general equilibrium framework and briefly discuss the possible tax incidence in the following scenarios:
a. A tax on petroleum products (tP).
b. A tax on labour in the non-petroleum industry (tLNP), where labour is perfectly mobile across sectors. (Hint: Draw a diagram to show the output and factor substitution effects, as we did in class.)
c. A tax on labour in the non-petroleum industry (tLNP), where labour is perfectly immobile across sectors.
d. A general tax on capital (tK) where capital is perfectly immobile across sectors.
e. A general tax on capital (tK) where capital is perfectly mobile across sectors.
f. A general income tax (t).
Problem 4. Iran used to subsidise gasoline, leading to a price to consumers that was one-fifth of the market price (The Economist, 2007: 52-53). Some people believed that, since the main source of government revenue was from oil exports rather than collecting taxes, fuel subsidies did not have a distortionary effect on the economy.
a. Using a graph, indicate the income effect, substitution effect, equivalent variation (EV), subsidy paid and excess burden in terms of the value of non-gasoline products. (suppose PNG = 1 and PG = 1) (Hint: suppose there are two products, gasoline (G) and non-gasoline (NG). The horizontal axis shows quantity of gasoline and the vertical axis shows non-gasoline
products.)
b. Using your results from part a, explain the efficiency implications of this policy and whether you support this belief or not. (Use letters to refer to any area or distance on your graph)
c. Using the Pareto efficiency conditions, support your results in part b.
d. A few years ago, the government decided to remove the subsidies and pay direct transfers to the citizens. Using your graph in part a, show how this policy would affect your results.
e. Using the Pareto efficiency conditions, support your result in part d.