(25 points) One of the reasons why we have financial intermediaries is because of asymmetric information problems. In this exercise we will illustrate how the presence of asymmetric information can create market failures. Suppose that you save $1 that you would like to lend. You are willing to lend provided you get at least $1 back in expected value. There are two projects that need funding project_A and project_B. If project_B gets 51 of funding, this project will earn $1.15 with certainty and it pays you back 1+r. If project_A gets funding, with probability 0.5 the project will succeed and it earns 51.8 and it pays you back 1+r; if the project fails it earns nothing and you lose the $1 of funding. Project_A and project_B will take a loan if the r is such that their expected profit is non-negative. a. (10 points) Suppose that you can tell project_A and project_B apart. Which of them will be able to secure funding, and at what range of interest rate? b. (10 points) Now suppose that you cannot tell project_A and project_B apart. You just know that there is a probability p you are dealing with project_B, and a probability 1p that you are dealing with project_A. Solve for a value of p at which neither project_A nor project_B will be able to get funding. c. (5 points) Why we said that there is a market failure? Why banks are better suited than you to give loans in a case like this