Consider the continuous investment model, with investment I yielding return RI = 101 in the case of success, and 0 in the case of failure. The entrepreneur starts with cash A. The probability of success is PH = 4/5 if the entrepre- neur behaves and PL = PH - Ap = 2/5 if he misbehaves. The entrepreneur obtains private benefit B = 18/5 per unit of investment if he misbehaves and 0 otherwise. (i) Write down the entrepreneur's optimisation problem. (ii) Derive the financing condition. (iii) Solve for the optimal contract, in particular determine the optimal level of investment I* (A), the return to the lender R (A) and to the entrepreneur, R₂ (A). (iv) Determine the equity multiplier k, the borrowing capacity d, and the shadow value of assets v. Explain.