Consider the market for corns in the US which is a perfectly competitive constant cost

industry. Suppose that each corn producer has a total cost function given by TC(q)=256+q^2, where this is both the short run and long run total cost function (note: for the short run TC(0)=256 while for long run TC(0)=0). Given the total cost function, a representative firm's marginal cost function is given by MC(q)=2q. The demand curve for corns in the US is given by MC(q)=2q. The demand curve for corns in the US is given by Qd^US = 5000-120P. Finally, assume for now that, due to high tariffs, there are no imports of corns into the US or exports of corns out of the US.

i).Derive the long-run equilibrium price and the equilibrium quantity both at the

firm level and at the industry level. Show work.

Assume everything as above except now there is free trade between the US and Canada,

i.e., tariffs equal zero. The demand curve for corns in Canada is given by Qd^C = 3000-60P, while there is no Canadian supply because weather conditions make it impossible to grow corns in Canada.

ii).If it costs zero to ship a unit of corns between the two countries, what are the long-run

equilibrium prices for corns in the US and Canada? Also, how many units are consumed in each country? Show work.

iii).Same question as in ii), but now assume that it costs 4 to ship a unit of corns

between the two countries. Be sure to show work and explain your reasoning.