The United States and Canada want to work together to reduce air pollution near Niagara Falls (which is on the border between the two countries). The United States can reduce pollution at a cost determined by the equation C = 2Q + 10, where C is the cost per ton of pollution reduction and Q is the quantity of pollution reduction, in tons. Canada can reduce pollution according to the equation C = 1/3 Q + 20.
a. One proposal is for the countries to reduce pollution by 100 tons each. Find the cost to the United States and the cost to Canada for this proposal.
b. Now imagine that this proposal includes a provision to trade pollution reduction between the countries? How much of a reduction will the United States make, and at what cost? How much of a reduction will the Canada make, and at what cost? How many permits will the United States buy from Canada?