Question

The demand for sunglasses is given by D(p) = 100 − 2 p and the supply curve is given by S(p) =3p

(a) Sketch both the demand and supply curves on the same graph (be sure to label your axes correctly)

(b) Determine the value of consumer surplus and producer surplus at the equilibrium values. show working

Suppose all sunglasses are imported from China.

Suppose also that the government imposes an import tariff of $10 per unit.

(c) Determine the new equilibrium values of price and quality. show working

(d) Determine the tariff’s impact on consumer surplus, producer surplus, and total surplus.

Answer 1

a) The required graph is given in figure 1

Figure 1

b) Equilibrium is where the demand and supply intersects.

100- 2p = 3p

5p = 100

p* = 20

q* = 60 units

Consumer surplus = area above the price line and below the demand line = 1/2 * (50-20)* 60 = $900

Producer surplus = area above the supply line and below the price line = 1/2 * 20 * 60 = $600

c) All 60 units are imported from China.

When an import tariff of $10 is imposed, then the price becomes $20+10 = $30. This means that the price cannot be more than $30. But the equilibrium price is $20 which is below this price. So, the import tariff does not have any impact on the price.

Therefore, new equilibrium price = $20 and quantity = 60 units

Figure 2

d) Since the price and quantity remains the same, the consumer surplus and producer surplus remains the same.