MSU is currently having Granger Construction build the $293,000$ square foot Student Recreation and Wellness Center on Harrison Road. Suppose the following paragraph describes the negotiation process between MSU and Granger Construction in early $2023.($The ground breaking occurred in September of $2023.)$ In this negotiation process, MSU first decides whether to negotiation a $$cost plus$$ contract with Granger or a fixed fee contract. A $$cost plus$$ contract is a contract that specifies a certain percent $($P$)$ that MSU will pay over Granger$$s cost and a fixed fee contact specifies a certain amount $($FF$)$ that MSU will pay Granger. If MSU selects a $$cost plus$$ contract, Granger than makes an offer of P which MSU can accept or reject. If MSU accepts, then Granger decides whether to build a high quality center or a low quality center. If MSU selects a $$cost plus$$ contract, Granger then makes an offer of P which MSU can accept or reject. If MSU accepts, then Granger decides whether to build a high quality center or a low quality center. If MSU selects a fixed fee contract, Granger then makes an offer of FF which MSU can accept or reject. If MSU accepts, then Granger decides whether to build a high quality center or a low quality center. If MSU rejects either the cost plus or the fixed fee contract, then Granger does not get the construction contract and MSU goes with another firm where they obtain a payoff of $$20$M $($M is million$).$ Suppose MSU is willing to pay a maximum of $$200$M for a high quality center and a maximum of $$165$M for a low quality center. Suppose Granger$$s cost of building a high quality center is $$150$M and Granger$$s cost of building a low quality center is $$119$M$.[$To make sure you understand how the $$cost plus$$ contract works, suppose Granger builds a high quality center and the agreed upon percent P is $5\%.$ In that case, MSU would pay Granger $(1+\mathrm{.}05)*150=$ $$157\mathrm{.}5$M$.$ If they agreed on a percent P of $5\%$ and Granger builds a low quality center, then MSU would pay Granger $(1+\mathrm{.}05)*119=$ $$124\mathrm{.}95$M$.]$ a$)$ Depict the extensive form of the $$game$$ described above $($i$.$e$.,$ the game tree$).$ b$)$ What is the Subgame Perfect Equilibrium of the game? $($You are welcome to indicate the Subgame Perfect Equilibrium on the game tree you depicted above. That said, you need to be precise and make sure you identify a strategy for each player.$)$ c$)$ What does this problem have to do with moral hazard?