Question $4$ Consider the following numerical example for adverse selection. There are two projects A and B$,$ and the investment of these projects are funded by bonds. Both projects need investment of $100.$ Project A earns $135$ for sure. Project B earns $150$ with probability $2/3$ and $0$ with $1/3.$ There$$s an investor requiring an expected return of $10\%.$ Answer the following questions.

a$.$ Suppose there is symmetric information. That means the investor is able to discern which project the fund is used to support. Which project will be financed? Why?

b$.$ Suppose there is asymmetric information, that is$,$ investor cannot tell whether the bond is to support project A or project B$.$ What is the required interest rate charged by the investor? Which project will be financed? Why?