A state government hired a contractor for a road construction project. The contractor's type, its cost efficiency, is known to the government. There is a 2/5 probability o its construction cost being 4 (billion dollars per lane) and 3/5 probability of the cost being 6. 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-2N^2/3. The government is interested in option N and writing a contract to maximize the benefit of 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 $4 billion dollars per lane and to choose "Contract H : Build NH lanes and get paid RH dollars" if its cost type is high cost $6 billion dollars per lane. Your analysis concludes that the optimal contract is "Contract L: Build ___A____ lanes and get paid __B___ billions dollars and "contract H ; Build __C____ lanes and get paid ___D___ billion dollars" Answer with two decimal places for lanes and one decimal place for billions of dollars. Please answer A, B, C, D
A state government hired a contractor for a road construction project. The contractor's type, its cost efficiency, is known to the government. There is a 2/5 probability o its construction cost being 4 (billion dollars per lane) and 3/5 probability of the cost being 6. 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-2N^2/3. The government is interested in option N and writing a contract to maximize the benefit of 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 $4 billion dollars per lane and to choose "Contract H : Build NH lanes and get paid RH dollars" if its cost type is high cost $6 billion dollars per lane.
Your analysis concludes that the optimal contract is "Contract L: Build ___A____ lanes and get paid __B___ billions dollars and "contract H ; Build __C____ lanes and get paid ___D___ billion dollars"
Answer with two decimal places for lanes and one decimal place for billions of dollars. Please answer A, B, C, D
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