4. When the railroads do not allow paid sick leave to employees, they reduce costs, and The railroads could pass on their savings to shippers in the form of lower rates, thereby putting downward pressure on a wide range of consumer prices, but that in fact the dominant rail firms feel little need to pass on the fruits of their efficiencies [no paid sick leave] to their customers.

a. Suppose the railroad market has two firms. The demand curve is P = 20 - 2Q₁ - 2Q₂, and the marginal cost to produce a railroad trip is 1 (in class we generally think about producing physical goods rather than services like a railroad trip, but you can treat services the same way we do physical goods). The firms compete in Cournot competition. What is the Nash equilibrium for the quantity each firm produces?

b. Recall from class that we solved the same problem with a marginal cost of 2 rather than 1, and we found that the Nash equilibrium was Q₁ = Q₂ = 3, which gave us a price of P = 20 - 2Q₁ - 2Q₂ = 20 - 6 - 6 = 8. Comparing our result from part a to our result of part b, how much did the price fall when MC fell by 1?

c. Based on what we found in parts a and b, how would you characterize the authors statement, the dominant rail firms feel little need to pass on the fruits of their efficiencies [no paid sick leave] to their customers? Its okay if your answer is not that the author is totally right or totally wrong.

d. For a comparison to Cournot competition, consider perfect competition with the same demand curve and cost function. When MC falls from 2 to 1, how much does the price fall?