Question

If the domestic demand curve is Q-10p-05 the domestic supply curve is Q=5p and the world price is $7.00, se calculus to determine the changes in consumer surplus, producer surplus, and welfare from eliminating free trade The change in consumer surplus (ACS) from eliminating free trade is (Enter your response rounded to two decimal places)

Answer 1

World price = $7

Domestic demand at world price (during free trade)

= 10*(P)^(-0.5)

= 10*(7)^(-0.5)

= 10*(0.37796)

= 3.7796 = 4 (approx.)

to get Consumer Surplus, integrate the equation of demand curve and substitute the values

consumer surplus = $10\frac{P^{0.5}}{0.5}$

= 20*(7)^0.5 = 52.915

Domestic Supply at world price (during free trade)

= 5*P^(0.5)

=5*(7)^(0.5)

= 5*(2.64575)

=13.2288 = 13 (approx)

to get producer Surplus, integrate the equation of supply curve and substitute the values

Producer Surplus = $5\frac{P^{1.5}}{1.5}$

= 5*[(7)^1.5]/1.5 = 61.7342

total welfare = Consumer Surplus + producer surplus

= 52.915 + 61.7342 = 114.6492

when free trade is eliminated

equilibrium price will be

Domestic Supply = Domestic Demand

5*(P)^(0.5) = 10*P^(-0.5)

P^(0.5+0.5) = 10/5

P = 2

Equilibrium Quantity in the case of elimination of free trade

Q = 5*(2)^(0.5)

= 7.071 = 7 (approx)

Consumer surplus when free trade is eliminated

consumer surplus = $10\frac{P^{0.5}}{0.5}$

= 20*2^0.5 = 28.2843

Producer surplus when free trade is eliminated

Producer Surplus = $5\frac{P^{1.5}}{1.5}$

= 5*[(2)^1.5]/1.5 = 9.4281

total welfare = consumer surplus + producer surplus

= 28.2843 + 9.4281 = 37.7124

Change in consumer surplus by eliminating free trade

= 28.2843 - 52.915 = -24.6307

consumer surplus is declined by 24.6307 units due to eliminating free trade

Change in producer surplus by eliminating free trade

= 9.4281 - 61.7342 = -52.3061

producer surplus is declined by 52.3061 units due to eliminating free trade

Change in total welfare by eliminating free trade

= 37.7124 - 114.6492 = -76.9368

Total Welfare is declined by 76.9368 units due to elimination of free trade

The change in consumer surplus from eliminating free trade is $ 24.63