13. The market demand curve for a good is x = 200 \text{\textendash} 3p. Suppose that there
are 10 small firms in the industry, where each firm has the identical short
run marginal cost function $MC = 5 + 2x_i$, with $x_i$ being the output of a
typical firm $i$. The marginal cost of the dominant firm is 5.
a) Calculate the short run equilibrium price and output of the industry.
What are the outputs of the dominant firm and a small firm?
b) Suppose that the long run marginal cost of a small firm is 20 and that
of the dominant firm is $0.1x_d$, where $x_d$ is the output of the dominant
firm. Determine the long run industry output, the output of a small
firm and the output of the dominant firm.