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xJudoEconomics (Inspired by the events in the Montreal cement market in 1966.) You are the CEO of Independent Cement (IC), and are considering whether and how to enter the Montreal market. If you enter, you must first choose whether to build a small plant that can serve up to 100 customers, or a large plant that can serve all 400 customers in the Montreal metropolitan area; in either case, the cost of the plant is $300 and the marginal cost of producing one unit of cement is $3. There are 400 total customers in the Montreal area, all of which value one unit of cement at $12. The current incumbent producer is Canada Cement (CC), who has a marginal cost of production of $4. If you enter, you must choose how to price your cement (within the range $0-12). After you choose your price, CC will choose its price for cement (again, within the range $0-12). If you have built a small plant, and have a price no greater than CCs, you will sell up to your capacity, and CC will sell to all the other consumers; if CCs price is less than yours, than CC will sell to all 400 consumers. If you have built a large plant, and have a price no greater than CCs you will sell to all 400 customers; if CCs price is less than yours, CC will sell to all 400 customers. 1. If you build a large plant, what price will you choose for your cement (and why)? What price will CC choose as a function of your price (and why)? What are your expected profits?

2. If you build a small plant, what price will you choose for your cement (and why)? What price will CC choose as a function of your price (and why)? What are your expected profits? (7 points) 3. What size plant will you choose to build (if any)? Why? Be sure to explain your reasoning in both game-theoretic and economic term?

Please help me how to solve this problems.