In Solved Problem 20.5, a firm calculated the optimal level of monitoring to prevent stealing. If \(G=\$ 500\) and \(\theta=20 \%\), what is the minimum bond that deters stealing?

Data From Solved Question 20.5:-

Workers post bonds of \(B\) that are forfeited if they are caught stealing (but no other punishment is imposed). Each unit of monitoring, \(M\), raises the probability that a firm catches a worker who steals, \(\theta\), by \(5 \%\). A unit of \(M\) costs \(\$ 10\). A worker can steal a piece of equipment and resell it for its full value of \(G\) dollars. What is the optimal \(M\) that the firm uses if it believes that workers are risk neutral? In particular, if \(B=\$ 5,000\) and \(G=\$ 500\), what is the optimal \(M\) ?