Question

Suppose that, in the market for litres petrol, demand is given by P = 5 – 0.3Q, and supply is given by P = 1 + 0.1Q. Further, suppose that the government provides a $1 per litre subsidy for petrol.

A. Calculate the effect of the subsidy on the equilibrium price and quantity.

B. Calculate the change in producer surplus and consumer surplus that result from the provision of the subsidy.

C. Does total surplus to everyone in the economy increase or decrease as a result of the subsidy? Explain why and calculate the amount of the change. (include graph)

Answer 1

Demand curve: P = 5 – 0.3Q

Supply curve: P = 1 + 0.1Q

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Equilibrium before subsidy:

5 – 0.3Q = 1 + 0.1Q

4 = 0.4Q

Q = 10 units

P = $2 per unit

Consumer Surplus = 1/2 x 3 x 10 = $15

Producer Surplus = 1/2 x 1 x 10 = $5

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Effect of subsidy:

Supply curve shifts to the right

Demand curve: P = 5 – 0.3Q

Supply curve: P = 0.1Q

Equilibrium sfter subsidy:

5 – 0.3Q = 0.1Q

5 = 0.4Q

Q = 12.5 units

Ps = $2.25 per unit

Pb = $1.25 per unit

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New CS = 1/2 x 3.75 x 12.5 = $23.4375

New PS = 1/2 x 1.25 x 12.5 = $7.8125

Both CS and PS rise, due to the subsidy

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Total Surplus falls by the area of the Deadweight Loss, shaded in blue.

DWL = 1/2 x 1 x 2.5

DWL = $1.25

Old TS was CS + PS = 15 + 5 = $20

New TS is CS + PS - Govt. expenditure = 23.475 + 7.8125 - 12.5 = $18.75