Question

1. Suppose the supply and demand curves for wheat are given by:

S= 10P-7

D=13-5P

where P is the price of wheat per bushel, D is the quantity of wheat demand (in millions of bushels), and S is the quantity of wheat supply (in millions of bushels). Suppose the free trade price of wheat is $1.00 and that a tariff of $0.20 is being considered by the government. If the country is a small importer calculate the following: i. The value of the increase in producer surplus expected due to the tariff. ii. The value of the decrease in consumer surplus expected due to the tariff. iii. The value of the tariff revenue expected due to the tariff. iv. The value of the change in national welfare expected due to the tariff.

Answer 1

Equilibrium price and quantity before tariff:

Demand = Supply
10P - 7 = 13 - 5P So, P = 1.33; Q = 6.3 ((10*1.33) - 7 = 6.3)

Price and quantity under free trade:
Demand = 13 - 5*1 = 8
Supply= 10*1 - 7 = 3

Price and quantity when tariff is imposed: Price now = 1.20
Demand = 13 - 5 * 1.2 = 13 - 6 = 7
Supply = (10*1.20) - 7 = 5

The following graph is based on the data above:

(The graph has been scaled for clear readablity)

i. The value of the increase in producer surplus expected due to the tariff.
Increased PS = the green area of the trapezium, +PS = ((3+5)/2) * 0.2 = 0.80

ii. The value of the decrease in consumer surplus expected due to the tariff.
It is the area of the trapezium, (+PS, DWL, Revenue< and DWL shaded above) = (8+7)/2 * 0.20 = 1.5

iii. The value of the tariff revenue expected due to the tariff.
The yellow shaded area above: tariff amount 8 quantity imported after tariff = 0.20 * 2 = 0.40

iv. The value of the change in national welfare expected due to the tariff.
The grey triangles area above (½*0.2*2) + (½*0.20*1) = 0.20 + 0.10 = 0.30

Note: Lost consumer surplus = Gained PS + revenue + DWL
1.5 = 0.80 + 0.40 + 0.30