Paul decides to contract a company to build an extension to his house prior to putting it on the market. The effort that the company devotes to the project is verifiable. The value that Paul will get from selling his house is V=150,000+x where x is the value added from the extension. The value added by the extension is uncertain. Paul knows that the extension will increase the value of the house by 7,000 with probability 0.2 and by 10,000 with probability 0.8. Paul also knows that he is risk averse and that the company is risk neutral. After selling his house, Paul will get a utility u(V-p) where p is the price paid for the extension and where u(.) is increasing and concave. The contract that they sign allows for the possibility of setting different prices based on whether the extension leads to a value-added of 7,000 or 10,000. Let pH be the price Paul pays for the extension when the value-added is 10,000 and pL the price paid otherwise. Which of these statements is correct?

Question options:

Paul should pay prices pH and pL such that pH =(10/7) pL

Paul should pay prices pH and pL such that pH = pL + 3,000

Paul should pay prices pH and pL such that pH =4(pL)

Paul should pay the same price no matter what: pH = pL