Question

1. In the Australian market for tea, demand is given by P = 10 - 2Q and supply is P = 2Q. Q represents tonnes of tea per year. Suppose that the government provides a subsidy of $2 per ton of tea. The introduction of the subsidy will _______ consumer surplus by ________.

2. In the Australian market for coffee, demand is given by P = 10 - Q and supply is P = Q. Q represents tonnes of coffee per year. Suppose that the government imposes a tax of $1 per ton of coffee. After the introduction of the tax, the equilibrium price and quantity will be

3. Suppose that weekly demand for iron ore in Australia is given by P = 900 – Q, and supply is given by P = 2Q, where Q represents tonnes of iron ore. To support consumers, the government decides to impose a price ceiling of $400 per tonne. If the government agrees to buy any excess supply, it will have to spend _____ to buy _____ tonnes of iron ore.

Answer 1

(1) P = 10 - 2Q , P = 2Q and subsidy = s = $2

Before subsidy equilibrium:

Demand = Supply

10 - 2Q = 2Q

4Q = 10

Q = 2.5 and

P = 10 - 2(2.5) = $5

Consumer surplus before subsidy= CS₁ = (1/2) * (Maximum willingness to pay - Actual payment) * Quantity sold

= (1/2) * (10-5) * 2.5 = $6.25

After subsidy equilibrium:

New supply - P = 2Q - s

P = 2Q - 2

So,

10 - 2Q = 2Q - 2

4Q = 12

Q = 3 and

P = 10 - 2(3) = $4

Consumer surplus after subsidy= CS₂ = (1/2) * (Maximum willingness to pay - Actual payment) * Quantity sold

= (1/2) * (10-4) * 3 = $9

Change in consumer surplus = CS₂ - CS₁ = 9 - 6.25 = $2.75

Thus, The introduction of the subsidy will increase the consumer surplus by $2.75.

(2) P = 10 - Q, P = Q and tax = t = $1

After the tax is applied, the new supply curve is:

P = Q + t

P = Q + 1

New equilibrium is given by:

10 - Q = Q + 1

2Q = 9

Q = 4.5

and P = 10 - 4.5 = $5.5

After the introduction of the tax, the equilibrium price and quantity will be $5.5 and 4.5 units respectively.

(3) P = 900 - Q and P = 2Q

Price ceiling at P = $400

At P = $400, quantity demanded is:

400 = 900 - Q_d

Q_d = 900 - 400

Q_d = 500

At P = $400, quantity supplied is:

400 = 2Q_s

Q_s = 400/2

Q_s = 200

So, there is an excess supply in the market given by:

Excess supply = Q_d - Q_s = 500 - 200 = 300 tonnes

If government buys the excess supply,

Govenment expenditure = $400 * 300 tonnes = $120,000

Thus, if the government agrees to buy any excess supply, it will have to spend $120,000 to buy 300 tonnes of iron ore.