Question

A country imports 5 million pounds of sugar per year and domestically produces another 5 million pounds. The world price of sugar is 25 cents per pound, and unlimited quantities of sugar are available at that price—the world supply curve of sugar is perfectly elastic. Assuming linear schedules, economists estimate the price elasticity of domestic supply to be 0.3 and the price elasticity of domestic demand to be 0.15 at the current equilibrium.

a. Use the given price elasticity and market equilibrium data to derive the domestic sugar demand and supply equations, and graph your results.

b. If no sugar could be imported, compute and show (on the graph created for (a)) the equilibrium domestic sugar price and quantity.

c. Compute and show on your graph the change in Consumer Surplus and Producer Surplus that free trade makes possible. That is, compare the situation when no imports are allowed to the situation first described in the question.

d. How would you measure the efficiency consequences of placing a ban on all sugar imports?

Answer 1

(a) Assuming linear schedules, the domestic price elasticity of supply is 0.3, ie. dP and domestic price elasticity of demand is 0.15, ie. dP Q demand), at the current equilibrium, where price P is the world price $0.25, since there is unlimited supply, and the domestic supply is 5 (mil paund) and demand is 10 (5 produced plus 5 imported in mil pound). We can use the elasticity equations by applying a little calculus, to find the demand and supply equations. (negative indicating the law of We have P where P is $0.26, and Q is 5 mil pound, and hence쏩뿌03or 6and byfundarmental theorem af calcas we or s6P+. As we have Q and P, hence6-0,25or 33-e. Hence, have the supply equation is s -6P+3.5.Nso, we have dP 10 mil pounds, and hence dP 10 where P is $0.26, and Q is o 0.25 or dP 40 and again, by the or Qp6P Putting the Q and P undamental theorem af calculus, we have we have 10-6 0.2+cor 113.Hence, the demand equation can be putted as n-6P+11.5 The graph is as below Supp World upply

As can be seen, A is domestic production and B is domestic demand at the world price, and AB is imported (b) If no sugar could be imported, them the equilibri otally donestic. The demand is o6P+1. and the domestic supply is Qs-6P+3.. The domestic equilibrium is where quantity demanded is equal to quantity supplied, e. QQsor-6P+115-6P+3.5 8 12P/12 2/3 066 A this price, quantity demanded is O-6-2/3+11or +11.3ar h-7. The graph is shown as below, where at the Point E, is the equilibrium for if there was no import um consumption and production would be Domestic Deman Domest Suppl 0.5 World Supply Import 10 (c) The graph is as below.

Domest World Supply If there was no trade, the equilibrium would be at point E, and in that case, the consumer surplus CS) would be the area of triangle MKE which is 2 OKEC which is area af triangle CFE plus area af rectangle OCFK, which AIK. KE # -(23/12-2/3).(75-4.6675dolars, and he producer surplus is the red CEFE-2/3) (7.5-3.5)-/3 dollars plus OC OK -3.5-2/3-/dollars, which is 2 is 11/3-3.6fdollars. s free trade is allowed, the consumer us is area of triangle MEN, whchisMN NB (2/12-1/4).10 8.3 producers surplus is area of triangle CGA plus the area of rectangle ONGC, which CG.GA0.25 (5-3.5)-0.1ST5 dollars. dolars pluS ON OC-0.25 33087,which is 1.0625 Hence, the CS has increased by $3.645833 and the PS has decreased by $2.604168, after free rade (d) The efficiency consequence can be measured by change in total surplus, which is equal to CS plus PS. As in free trade, total surplus is $9.395833. In case trade is banned, the total surplus is $8.364166, and hence, the efficiency is said to be decreased if trade is banned, making a deadweight loss of change in tatal surplus, which is basically the area of triangle AEB, which bsse height-5y2/3-1/4) 1016which can be found as the change in the total is 2 surplus. What happens is, as the trade is banned, the area NAEK, which was the CS, is grabbed by the PS, but the area AEB is lef, and hence leads to deadweight loss.