Quantity demanded Qd = 10 + 2p , quantity supplied : Qs = 60 - 0.5p . They intercept at p = 20$/ton, Qd=Qs = 50. a) Assume that imports are available at price = 10. Find the equilibrium price and quantittes. b) Assume that exports are also available. The state taxes 16$/ton on imports and subsidizes 16$/tn the exports. Find the new equilibrium price and quantities.
My solution
a)For p =10 , Qs = 10 + 2*10 = 30 and Qd = 60 - 0.5*10=55 so there is a domestic shortage of 55-30 that must be covered with imports. So imports are 55-30 = 25. So equilibrium price = 10 and equilibrium quantity produced domestically is 30
b) Subsidy of 16 means that domestic price (20$/ton) falls to 4$/ton while tax on imports means that world price (p=10$/ton) is seen domestically as 26$/tn. So domestic demand is Qd = 60 - 0.5*4 = 58 and domestic supply is Qs = 10+2*4 = 18 so there are 58-18=40 of imports.
So newequilibrium price is 4 and equilibrfium domestic quantity produced is 18.
Answers & Comments
Verified answer
You may have got the question written wrongly with demand and supply equations interchanged.
I assume that you have quoted the equations in your solution correctly: demand curve should be negatively sloped while supply curve should be positively sloped. If that is so, the answer to part a) seems ok. But for part b), I have a doubt. Imports are taxed at $16/ton and if the domestic producers are subsidized if they export at the same rate, the price they get on exports is international price + 16. Technically they can export the entire produce at $10 and also get $16 per ton. So, the supply equation would give a supply of Qs = 10+2*26 = 62. Since the domestic suppliers would not supply at anmy price lower than the cost of imported material, the ruling price would be $26. Hence domestic demand would be Qd = 60 - 0.5*26 = 47. Hence there would not be any imports. Exports would be domestic demand minus domestic demand = 62- 47= 15.
Please check your answers again.