This entrepreneur has no collateral and needs to borrow the $3$ million cost. The risk$-$free interest rate is zero. Venture capital investors are indifferent to risk, but each has only $300,000$ of capital to invest. They can only ensure that the distribution of returns is as described in $($a$)$ either $($i$)$ by each incurring a non$-$financial monitoring cost equivalent to $125,000$ or $($ii$)$ by jointly inflicting a non$-$financial penalty worth $4$ million upon the entrepreneur if she defaults. Show that method $($i$)$ is the most cost$-$effective way of securing this distribution of returns.