I’m working on an economics question and need an explanation to help me understand it better.
Please show your work and explain your answers.
1. Tacitus can choose either a safe or a risky project. To keep things simple, let’s say either project costs $100. A safe project yields $110 with certainty, while a risky project is equally likely to yield $200 or zero. Tacitus needs financing for 50 percent of the cost of his project. Lenders cannot observe his choice of project. Everyone is risk-neutral, and the risk-free rate is 4%.
a. If Tacitus were to sell $50 worth of bonds with a face value equal to $52, in which project would he invest? Justify your answer. How much would bondholders get paid, on average?
b. How much face value would Tacitusneed to offer lenders in order to sell $50 worth of bonds?
c. Is Tacitus willing to offer the face value required to sell bonds? Explain.
d. Is Tacitus willing to finance a project by selling shares? Are savers willing to purchase his shares? Does financing with equity yield an efficient equilibrium?
2. Pompeia wants to finance her education, plus buy a home. She needs to borrow $400,000, and the risk-free rate is 5%. She can try to obtain financing by selling either debt or equity. Pompeia’s job pays a salary of $60,000 per year. If she works hard, she has a 50 percent chance of getting a promotion and an increase in her salary to $140,000. If Pompeia devotes minimal effort to her job, her salary will remain at $60,000. Pompeia’sdisutility of working hard is $36,000. Everyone is risk-neutral, and all the surplus goes to Pompeia. Assume asymmetric information.
a. How much is Pompeia’s annual cost of funds?
b. Hard work generates how much surplus? Explain.
c. In an equity sale, Pompeia must try to sell at least a 1/5share. Why?
d. If savers were to accept a 1/5 share, would Pompeiawork hard? Show your computations. How big a share do savers require?
e. In equilibrium, does she obtain financing by using debt or by using equity? Show your computations. Is the equilibrium efficient?
f. Describe the asymmetric information problem: Who can’t observe what?
g. Would savers accept a 1/5 share if the information were symmetric? Explain.
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