Borrower: Isaac is an aspiring entrepreneur in Uganda. He is deciding between two investment projects. Both projects are risky and require an investment of $100. He does not have any money, so he needs a loan in order to undertake one of the projects. He will take a loan as long as he can earn expected income of at least zero. The two projects have the following characteristics:

Project 1 consists of opening Take-A-Wakanda-Wild-Side, a tourist company that provides guided walking tours through Bwindi National Park in southwest Uganda, where the movie BlackPanther was filmed. Given the worldwide popularity of Black Panther, this project is relatively safe: with 70% probability, it succeeds and generates $240 of revenue, and with 30% probability,it fails and generates only $100 of revenue.

Project 2 consists of opening Afri-CAN!, a factory that makes recyclable cans using the shells from ground nuts (peanuts) that are typically discarded by farmers in Uganda. This project is much riskier a s climate change has increased the risk that the ground nut harvest fails in Uganda. Specifically, with 30% probability, it succeeds and generates $400 of revenues, and with 70% probability, it fails and generates only $60 of revenues.

Lender: Anderson is Isaacs rich friend who may offer Isaac a loan. If Anderson offers Isaac the loan, he would have to withdraw $100 from his savings account where he is currently earning a 10% interest rate. According to local regulations, loans in Uganda are limited liability and work as follows. If Isaacs project succeeds, he must repay 100% of the debt obligation (principal plus interest); however, if his project fails, he only has to repay 50% of the total debt obligation. For example, if the interest rate is 30%, Isaac would have to repay 0.50*(1+0.3)*100 if his project fails.

Known:

Isaac's objective functions

E(y1) = 98 - 100i

E(y2) = 62 - 100i

Anderson's Objective Functions

E(1) = 85i - 25

E(2) = 65i - 45

(d) If the credit market is characterized by perfect competition: i. What is the equilibrium interest rate charged by Anderson? ii. Which project does Anderson make Isaac do? iii. How much expected profit does Anderson earn from the equilibrium contract? iv. How much expected income does Isaac earn from the equilibrium contract? (d) If the credit market is characterized by perfect competition: i. What is the equilibrium interest rate charged by Anderson? ii. Which project does Anderson make Isaac do? iii. How much expected profit does Anderson earn from the equilibrium contract? iv. How much expected income does Isaac earn from the equilibrium contract