Question: We've claimed that the efficient way to spread out work across firms in the same industry is to set the marginal cost of production to be the same across firms. Let's see if this works in an example. Consider a competitive market for rolled steel (measured by the ton) with just two firms: SmallCo and BigCo. If we wanted to be more realistic, we could say there were 100 firms like SmallCo and 100 firms like BigCo, but that would just make the math harder without generating any insight. The two firms have marginal cost schedules like this:
a. We'll ignore the fixed costs of starting up the firms just to make things a little simpler. What is the total cost at each firm of producing each level of output? Fill in the table.
b. What's the cheapest way to make 11 tons of steel? 5 tons?
c. What would the price have to be in this competitive market for these two firms to produce a total of 11 tons of steel? 5 tons?
d. Suppose that a government agency looked at BigCo and SmallCo's cost curves. Which firm looks like the low-cost producer to a government agency? Would it be a good idea, an efficient policy, for the government to shut down the high-cost producer? In other words, could a government intervention do better than the invisible hand in this case?
e. Let's make part d more concrete: What would the total cost be if BigCo were the only firm in the market, and it had to produce 7 tons of rolled steel? What would marginal and total costs be if SmallCo and BigCo let the invisible hand divvy up the work between them?
