In State College, the demand for bottled spring water is given by Q = 121 − P 2 . There is one known spring in town controlled by the bottler First Spring (FS). In other words, FS is a monopolist in the market for spring water. FS’s cost of production for gallons of water is C(Q) = 2Q. Suppose now that a new spring is discovered in State College. A bottler called New Spring (NS) gains exclusive rights to this spring and is deciding whether or not to set up operations and compete with FS. If NS decides to join the market, NS and FS will be Cournot competitors. Both firms will face the same production costs, whereby C(Q) = 2Q. Nevertheless, NS will have to pay a one time set up cost of $2,000.
1. Write down NS’s profit maximization problem. What is its optimal level of production as a function of FS’s production decision? (hint: its best response).
2. How does the incumbent FS respond to NS’s entry? Does its level of production increase, decrease, or stay the same?
3. Find the Cournot-Nash equilibrium level of production in this market. What is the equilibrium price of a gallon of water? What are each bottler’s respective profits?
4. By how much does consumer surplus in this market change as a result of New Spring’s entry into the market? What about total industry profits?
5. Suppose that, right before setting up, both firms learn that New Spring had underestimated the one time setup cost. A new estimate reveals this one time set-up cost is actually $3,600. How do the market equilibrium quantity and price change in light of this new information? What about total industry profits?
6. Suppose that consumers created a Spring Water Authority (SWA) that would subsidize set up costs for new entrants. This subsidy would be funded directly (e.g. dollar-for-dollar) out of consumers’ surplus. Would consumers want the SWA to subsidize the set-up costs for New Spring? What would be the optimal amount of this subsidy? Explain.
7. Suppose that some time after New Spring is in operation, 3rd Spring is discovered near State College. 3rd Spring faces the same technology as its predecesors (e.g. C(Q) = 2Q) and a setup cost of $3,600. Would consumers vote to subsidize 3rd Spring’s set up costs? If so, what is the optimal level of subsidy?