econ: price floor and price ceiling
Economics

Tutor: None Selected  Time limit: 1 Day 
Suppose the government imposes a price ceiling of $50 on a market characterized by the following information:
Qd=7002P Qs=100+4P
Calculate the magnitude of deadweight loss from the price ceiling. Find a price floor that will result in the same magnitude of deadweight loss
I'm not going to do the problems for you but here's how I would do them:
In your first question: The price that the domestic consumer and the domestic producer see are the same as the international price before the quota. So set the international supply and demand curves equal to each other to find the price at which they are at equilibrium, this is the international price before the quota.
To find the price after the quota, you need to find the supply and demand after the quota. To do this you need to realize that the quantity demanded by the domestic consumer will be X quantity more than the amount supplied by the domestic producer, where X is the size of the quota (in your case it's 16 million). Set these two equal to each other to find this price. So in your example the supply and demand curves look like this for the domestic market
Qd = 200 – 40P [Demand]
Qs = 40 + 40P [Supply]
But we know that Qd = Qs + 16, so
Qs + 16 = 200 – 40P [Demand]
Qs = 40 + 40P [Supply]
then you can solve for Qs in terms of P, or P in terms of Qs, etc.
Hopefully you know what consumer and producer surplus are, and if you don't I don't want to explain it to you. Now find the change in the (sum of the consumer surpluses plus the producer surpluses). So it'd be (Consumer Surplus after the quota + Producer surplus after the quota) minus (Consumer Surplus before quota + Producer Surplus after the quota). The fact that this quantity is negative means that this is a net loss in "happiness" or whatever by both parties, making this a deadweight loss
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