Problem - 100 individuals live in a market and possess utility functions defined over two goods, x and y. The utility function of each individual is given by U(x, y) = x + y. Each individual faces the same prices of the two goods, px and py, each has an income of I = 1, and the price of good y is 1. There exists a large number of "potential" entrants into the industry, and each has a total cost function given by TC(qx) = 10qx - 4q2 x + q3x.
(a) Define the market demand function for good x (remember that py = 1 and each individual has an income of 1).
(b) Determine the number of firms that would produce the good x in a long-run competitive equilibrium (HINT: The correct answer to this question belongs to the set {0, 1, 2, ...}).