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November 22, 2014

Homework Help: college: ECON

Posted by anonymous on Saturday, June 5, 2010 at 9:21pm.

Pedro is a rice farmer. In order to grow rice, he needs $100 to buy seeds. Rice production is risky. If it turns out to be a GOOD year, Pedro has a harvest worth $500. If, instead, he has a BAD year, Pedro’s harvest is worth $0. Assume throughout this question that Pedro is risk neutral.
After Pedro plants the seeds, he must decide how hard to work. He has two choices: WORK HARD or BE LAZY. By working hard, Pedro can make a GOOD year more likely. Specifically, if he chooses WORK HARD, he will have a GOOD year with 80% probability while if he chooses to BE LAZY, he only has a 20% probability of having a GOOD year. Table 1 summarizes Pedro’s situation:
Table 1. Summary of Farming Parameters
Action
Probability of Success
Value of Harvest under Success
Probability of Failure
Value of Harvest under Failure
WORK HARD
.8
$500
.2
$0
BE LAZY
.2
$500
.8
$0
For part (a), make the following two assumptions: First, Pedro has $100 so that he can buy the seeds and plant rice. Second, working hard doesn’t impose any cost on Pedro.
a. Let Y denote Pedro’s profit (value of harvest minus costs). What is the expected value of Pedro’s profit if he chooses to WORK HARD?
b. What is the expected value of his profit if he chooses to BE LAZY?
For part (c), still assume that Pedro has $100, however let’s be more realistic about the cost of working hard. Specifically, for all remaining parts of this problem assume that WORK HARD imposes a cost on Pedro that is the equivalent of paying $240. You can think of this $240 cost exactly like the monetary cost of buying an input. BE LAZY, on the other hand, imposes no cost on Pedro.
c. Now what is the expected value of Pedro’s profit if he chooses to WORK HARD?
d. What is the expected value of his profit if he chooses to BE LAZY?
e. Which action (WORK HARD or BE LAZY) will Pedro choose?
Now assume that Pedro does not have $100 to finance production. Instead he needs to go to a bank to get a $100 loan. Assume that the banking industry is competitive so that any loan that is made should earn the bank zero expected profits and the bank’s opportunity cost of lending is zero. (In other words, the expected value of repayment – which is interest plus principal -- to the bank should be $100.) Also assume that Pedro repays the loan only if the harvest is successful.
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f. If a bank could give a loan AND be certain that Pedro would WORK HARD, what interest rate, i, would the bank charge?
g. If instead the bank gave a loan and was certain that Pedro would BE LAZY, what interest rate would the bank charge?
Now assume that the bank faces moral hazard – they cannot observe the action that Pedro takes.
h. Now what interest rate must the bank charge in order to earn zero expected profit? (HINT: For a given interest rate, the bank will compute Pedro’s expected profit from the two different actions. It will then use this information to decide the interest rate it charges.)
i. If Pedro doesn’t farm, he earns $10 with certainty. Given your interest rate from part (h), will Pedro want the loan? Explain your answer.
j. Define a “market-failure”? Given your answers above, discuss how asymmetric information in credit markets could lead to a market failure. (If you’re not sure about your answers to (a) – (i), you can answer this part independently.)

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