Economics – Consumer and producer surplus | e-Consult

1. Calculate Equilibrium Price and Quantity:

Equilibrium is found where Demand = Supply. Therefore: 100 - 2Q = 10 + Q. Solving for Q: 90 = 3Q, so Q = 30. Substituting Q=30 into either equation gives P = 10 + 30 = 40. Therefore, the equilibrium price is £40 and the equilibrium quantity is 30 units.

2. Calculate Consumer Surplus:

Consumer surplus is the area of the triangle above the price and below the demand curve. The height of the triangle is the difference between the intercept of the demand curve (when Q=0) and the equilibrium price (P=40). The intercept of the demand curve is P=100. Therefore, the height is 100 - 40 = 60. The base of the triangle is the equilibrium quantity (Q=30). So, Consumer Surplus = 0.5 * base * height = 0.5 * 30 * 60 = £900.

3. Calculate Producer Surplus:

Producer surplus is the area of the triangle below the price and above the supply curve. The height of the triangle is the difference between the equilibrium price (P=40) and the intercept of the supply curve (when Q=0). The intercept of the supply curve is P=10. Therefore, the height is 40 - 10 = 30. The base of the triangle is the equilibrium quantity (Q=30). So, Producer Surplus = 0.5 * base * height = 0.5 * 30 * 30 = £450.

4. Impact of a £10 Tax:

The tax shifts the supply curve upwards by £10 per unit. The new supply curve is P = 20 + Q. The new equilibrium is found where Demand = New Supply. Therefore: 100 - 2Q = 20 + Q. Solving for Q: 80 = 3Q, so Q = 26.67 (approximately). Substituting Q=26.67 into either equation gives P = 10 + 26.67 = 36.67 (approximately).

New Consumer Surplus: The height of the triangle is 100 - 36.67 = 63.33. The base is 26.67. New Consumer Surplus = 0.5 * 26.67 * 63.33 = £840.00 (approximately). Consumer surplus decreases.

New Producer Surplus: The height of the triangle is 40 - 36.67 = 3.33. The base is 26.67. New Producer Surplus = 0.5 * 26.67 * 3.33 = £44.99 (approximately). Producer surplus decreases.

Conclusion: The tax reduces both consumer and producer surplus. The consumer surplus decreases because the price paid by consumers increases. The producer surplus decreases because the price received by producers decreases. The net loss to society is the difference between the original consumer and producer surplus (£900 - £450 = £450) plus the tax revenue (£10 * 26.67 = £266.70) which is a net loss of £183.30.