1. Consider the following model of the market for petrol, which is perfectly
competitive and has the demand and supply curves:
where Qd is quantity of petrol demanded, Qs is the quantity of petrol supplied,
and P is the market price of petrol.
- (a) What does it mean for markets to clear? Find the market-clearing price and quantity of petrol.
- (b) Define the concepts of consumer surplus and producer surplus. What is the consumer and producer surplus at the market-clearing price?
- (c) Define the concept of point elasticity of demand and supply. At the marketclearing price and quantity, what is the point elasticity of demand? What is the point elasticity of supply?
- (d) Suppose that the government puts a tax of $4 on each unit of petrol consumption. How much revenue tax does this tax raise? What is the deadweight loss of the petrol tax?
- (e) Now suppose that instead of taxing consumption, the government puts a tax on production of each unit of petrol. Repeat part (d). Define the concept of the incidence of a tax. Who bears the burden of a petrol tax on consumption or production: consumers or producers? If the demand curve for petrol was less elastic, and the supply curve for petrol was more elastic, what would happen to the incidence of the petrol tax? Explain, using a diagram.
- (f) Define the concept of a negative externality. Suppose that petrol consumption causes pollution, and that there is a negative external marginal cost of $2 associated with the pollution that occurs as a result of petrol consumption. What is the efficient quantity of petrol consumption and production? In the absence of the petrol tax, is the free market outcome efficient? Explain. What is the total cost of pollution at the efficient quantity? Carefully explain why, even though petrol consumption causes pollution and that there is a negative external marginal cost of $2 associated with petrol consumption, the efficient level of petrol consumption is not zero.
- (g) With the petrol tax of $4 in place, is the market outcome efficient? What is the deadweight loss of the $4 petrol tax in this situation?
- 2. Suppose that the market for insulation batts is perfectly competitive and can
be described by the following demand and supply curves:
- (a) Draw the demand and supply curves based on the above equations.
- (b) Find the market-clearing price and quantity of insulation batts.
Now suppose that the government implements a policy of subsidising insulation batt purchases. The subsidy is set at $10 and is paid to consumers.
- (c) Find the new market-clearing quantity. With the subsidy in place, what price do consumers pay? What price do producers receive? What is the change in consumer surplus? What is the change in producer surplus? How much revenue does it cost for the government to run this subsidy scheme? What is the deadweight loss of the insulation subsidy, and why does it arise in the case of a subsidy?
- (d) What is the incidence of the subsidy? In general, how do the incidence and deadweight loss of a subsidy depend on the elasticities of demand and supply? (Hint: Draw a diagram to show your answer).
- 3. Suppose that there are two markets, A and B. These goods are neither substitutes nor complements, so an increase in the price of one good as no effect on demand for the other good, and vice versa.
The supply curves for both goods are perfectly elastic, with marginal costs constant and equal to 1 in both markets.
The demand curves for these two goods are as follows:
- (a) Find the initial market-clearing prices and quantities in each market. At these market-clearing prices, what is the point elasticity of demand in each market?
- (b) Suppose that the government introduces a tax of $1 in market A, and $1 in market B. How much revenue does this combination of taxes raise? What is the deadweight loss of this combination of taxes?
- (c) Now suppose that you wanted to raise the same (or more) tax revenue that you found in part (b), but that you also wanted to reduce the overall deadweight loss of the tax system. Is there some other combination of taxes that allows you to achieve this goal? Explain your answer, using the elasticity of demand.
- 4. This question considers the effects of government purchases on market prices, quantities and welfare. Consider the market for cars, which is perfectly competitive and is described by the following demand and supply curves:
(a) Find the market-clearing price and quantity. What is the producer and consumer surplus at this market-clearing price?
Now suppose that the government needs to purchase 20 cars, no matter what the price it has to pay. In other words, the government's demand curve for cars is perfectly inelastic at the quantity of 20.
- (b) The new market demand curve is the horizontal sum of the private demand curve and the new government demand curve. On a diagram, plot the old demand curve, the new demand curve, and the supply curve. Find the new market-clearing price and quantity.
- (c) As a result of the government purchase programme, what happens to the producer surplus? What happens to the consumer surplus of those who purchase cars for private use? Who benefits from the government programme to purchase cars, and who loses? Do the benefits outweigh the losses? Explain.
- (d) How much does the government spend on car purchases if it has to purchase 20 cars at the new market-clearing price? The amount of government spending is often used as a measure of the economic benefits of that spending. Explain why the amount that the government spends on cars is a very poor and inaccurate estimate of the economic benefits of the car purchase programme.
- (e) 'Crowding out' refers to the reduction in private quantity demanded that occurs when government purchases goods on private markets. What is the extent of crowding out in this case?
Some economists use the term 'multiplier' to describe the effect of government purchases on output. The multiplier is defined as the increase in output divided by the increase in government demand. Calculate the multiplier in this case.
(f) How do the multiplier and the extent of crowding out depend on the elasticities of demand and supply? (Hint: draw a diagram to show your answer.) Under what circumstances is the multiplier 1, and what is the extent of crowding out and the economic benefits of the car purchase programme in this case? Under what circumstances is the multiplier zero, and what is the extent of crowding out and the economic benefits in this case?