The US president and Canadian prime minister are considering an environmental treaty to clean up the Great Lakes. Canada currently dumps 30m tons of a certain kind of effluent into the lakes per year, and the US dumps 40m tons. The US president is concerned that reducing American effluent to less than 40m tons will place heavy costs of cleanup on US industry, so his ideal point is that the US dumps 40m tons and the Canadians reduce their effluent to 0. Likewise, the Canadian prime minister’s ideal point is that Canada continues dumping 30m tons, but that the US reduce its dumping to 0.
Assume that country i’s utility is captured by the quadratic loss function:
ui = -(x - zi)2 - (y - wi)2
where x is the amount of effluent (in million of tons) that the U.S. dumps into the Great Lakes per year, y is the amount of effluent that Canada dumps per year, and zi and wi are person i's ideal point for the US and Canadian effluent levels, respectively. (Note: If you need a refresher on the quadratic loss function, you may want to refer to your notes or the cloud recording from lecture on September 28).
Without cooperation the two leaders set their policy at their own ideal point for their own effluent level. Therefore the status quo is the policy outcome (40, 30).
a. Calculate the US president’s utility from the status quo.
b. Calculate the Canadian prime minister’s utility from the status quo.
c. Let’s assume that the U.S. and Canada reach an agreement to set the US effluent level at 20m tons and the Canadian effluent level at 15m tons. What is the US president’s utility if both countries abide by this agreement?
d. What is the Canadian prime minister’s utility if both countries abide by this agreement?
e. Of course, both sides might not abide by the agreement. What is the US president’s utility if the US abides by this agreement, but Canada does not (in other words Canada cheats)?
Sample Solution