The industry of motion picture is undermonopolistic competition.We assume that each firm produces one variety of motion picture. The production of each variety is symmetric. Each variety needs 20,000,000 US dollars as the fixed cost, and needs 3 US dollars as marginal cost (per ticket).

Let be the number of varieties of motion picture, be the price. The demand facing any one firm ()is given by whereis the total ticket sales of the market andis the average price of the market. The total ticket sales in US are 1,600,000,000 and the total ticket sales in China are 900,000,000.

1) Assume the demand facing any one firm is linear. DERIVE the relationship between price ()and the number of varieties (.

2) Assume that China does not import motion picture from other counties. Find the number of varieties and the price of motion picture in China.

3) suppose that China and US establish a free trade agreement that removes all the trade barriers in motion picture between these two countries. Find the number of varieties and the price of motion picture for Chinese consumers.