Consider an entrepreneur, Mr. David Barnes, who borrows $100 at t = 0 (the start of the period) and invests the loan in a project that will pay off at t = 1 an amount $300 in the successful state (state S₁) and nothing in the unsuccessful state (state S₂) for his start-up firm, Barnes Manufacturing. The probability of S₁ is p (e), where e is Mr. Barnes’ effort in managing the project. Mr. Barnes can choose one of two effort levels: high (h) or low (l). Mr. Barnes sustains a personal cost of $40 to expend h and nothing if l is chosen. Assume p (h) = 0.8 and p (l) = 0.6. Mr. Barnes has collateral available, but collateral worth $1 to him is worth 90 cents to the bank. Assume that the bank cannot observe Mr. Barnes’ choice of effort. The riskless interest rate is 10%. Compute the optimal loan contract.