QUESTION 5 A state government hired a contractor for a road-construction project. The contractor's type, its cost efficienciency, is unknown to the government. There is 2/3 probability of the its construction cost being 3 (billion dollars per lane) and 1/3 probability of the cost being 5. More lanes yield more social benefit in the form of faster travel and fewer accidents. The social value V (measured in billions of dollars) from having N lanes on the highway is: V=15N-N2/2. The government is interested in choose N and writing a contract to maximize the benefit to the state (V) net of the fee paid to the contractor (call it F); G=V-F. Your goal as a government official is to design a pair of contracts to separate the types of contractor. You want the contractor to choose "Contract L: Build N lanes and get paid RL dollars" if its cost type is low cost of $3 (billion dollars per lane) and to choose "Contract H: Build NH lanes and get paid RH dollars" if its cost type is high cost $5 (billion dollars per lane). The state government must satisfy the voluntary participation constraints so that each type of a contractor accepts the contract: N R for a low cost contractor, and R N for a high cost contractor. Hint: Type either H. L. or numbers in the blanks