Assume that the demand for chalk is p = 8 -0.1, where P is the market price and Q is the total market output measured in thousands of boxes of chalk. Suppose that there are three firms in this industry, each of which has a constant variable cost of $2. Each firm choose its own output level, qi, and takes whatever price the market determines. To simplify the problem, each firm can choose from three levels of output (in thousands): low ( q1 = 8), medium ( q1 = 10), or high ( q1 = 12), with fixed costs (in thousands) of $2, $4, and $4, for low, medium, and high output, respectively. Assume, for simplicity, that all other firms choose the same output level (as each other), so that low ( q2= 24), medium ( q2= 30), or high ( q2= 36).
a. Construct a payoff table for this game, using profits per firm as the payoffs.
b. Identify all pure strategy Nash equilibrium (if any exist).
c. Describe the competitive nature of this industry. How might this change if each of the other firms can independently choose their output level? What is each firm likely to choose? What implication(s) would this have for other firms?