Question

The market demand function for corn is Q(d) = 30- 2P and the market supply function is Q(s)= 5P - 2.5, both measured in billions of bushels per year. Suppose the import supply curve is infinitely elastic at a price of $3.50 per bushel.

a. Calculate consumer surplus, producer surplus, and aggregate surplus.

b. Whatwouldbethewelfareeffectsofatariffof$1.00perbushel?

Answer 1

Answer (a) - The market demand for corn is Qd = 30 - 2P and the marekt supply function is Qs = 5P - 2.5. The equilibrium price in the market will be determined where quantity demanded equal to quantity supplied. We need to know what demand is and supply at price on which import demand curve is perfectly elastic. Price is $3.50 per bushel where import demand curve is perfectly elastic.

Place value of 'P' into demand curve, P = $3.50

Qd = 30 - 2*3.50

Qd = 30 - 7

Qd = 23 bushel

Domestic supply at price $3.50 per bushel,

Qs = 5*3.50 - 2.5

Qs = 17.5 - 2.5

Qs = 15 bushel

We can see that demand exceed supply of corn by 8 bushel of corn. The economy will import 8 bushel of corn.

Consumer surplus = 1/2 * (15-3.50)* 23

CS = 1/2*11.50 * 23

CS = $132.25

Producer surplus = 1/2 *(3.50 -0.5 )* 17

PS = 1/2*3*17

PS = $25.5

Total surplus = CS + PS

Total surplus = 132.25 + 25.5

Total surplus = $157.75

(b) Suppose tariff has been imposed on corn imports by $1.00. Now import supply curve would perfectly elastic on price (3.50 + 1 = $4.50) per bushel.

Now place 'P' equal to $4.50 into demand and supply equation. Quantity demanded after tariff is 'Qd1'

Qd1 = 30 - 2*4.50

Qd1 = 30 - 9

Qd1 = 21 bushel

The supply would be Qs1 after tariff imposition.

Qs1 = 5*4.5 - 2.5

Qs1 = 22.5 - 2.5

Qs1 = 20 bushel

Now consumer surplus after tariff is

CS1 = 1/2 * (15 - 4.5) * 21

CS1 = 1/2 *10.5*21

CS1 = $110.25

Producer surplus (PS1) = 1/2 *(4.5 - 0.5) * 20

PS1 = 1/2*4 * 20

PS1 = $40

Total surplus = CS1 + PS1

Total surplus = 110.25 + 40

Total surplus = 150.25

Total welfare effect = total surplus after tariff - total surplus before tariff

Total welfare effect = 150.25 - 157.75

Total welfare effect = -$7.5

This is total welfare effect of tariff. Total surplus has been reduced by $7.5.