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.)
The answer is true or false.
Are you still looking for the answer.
Which of the following is not economic investment?
(a). The purchase of 100 shares of AT&T by a retired business executive.
(b). The purchase of a drill press by the Ajax Manufacturing company.
(c). Construction of a suburban housing project.
(d). The piling up of inventories on a grocer's shelf.
To answer these questions, we need to calculate the expected value of Pedro's profit for each action (WORK HARD or BE LAZY) under different assumptions. Let's go step by step.
a. To find the expected value of Pedro's profit if he chooses to WORK HARD, we multiply the probability of success (0.8) by the value of the harvest under success ($500) and subtract the cost of buying seeds ($100):
Expected profit of WORK HARD = (0.8 * $500) - $100 = $400 - $100 = $300.
b. To find the expected value of Pedro's profit if he chooses to BE LAZY, we multiply the probability of success (0.2) by the value of the harvest under success ($500) and subtract the cost of buying seeds ($100):
Expected profit of BE LAZY = (0.2 * $500) - $100 = $100 - $100 = $0.
c. Now, assuming that WORK HARD imposes a cost on Pedro of $240, the expected profit of WORK HARD becomes:
Expected profit of WORK HARD = (0.8 * $500) - $240 - $100 = $400 - $240 - $100 = $60.
d. The expected profit of BE LAZY remains the same as before because there is no cost associated with it:
Expected profit of BE LAZY = (0.2 * $500) - $100 = $100 - $100 = $0.
e. Pedro will choose the action that yields the higher expected profit. In this case, he will choose to BE LAZY since the expected profit of BE LAZY is $0, while the expected profit of WORK HARD is only $60.
f. Since the bank can be certain that Pedro will WORK HARD, they know that Pedro will have an expected profit of $60. But since the bank's opportunity cost of lending is zero, it will charge an interest rate that makes the expected repayment equal to $100. Therefore, the interest rate would be:
Interest rate = ($100 - $60) / $100 = 40%.
g. Similarly, if the bank can be certain that Pedro will BE LAZY, they know that Pedro will have an expected profit of $0. The interest rate would be:
Interest rate = ($100 - $0) / $100 = 100%.
h. In order to earn zero expected profit, the bank needs to charge an interest rate that makes the expected repayment equal to $100. Since the bank cannot observe Pedro's action, it needs to consider the expected profits from both actions. The highest expected profit Pedro can have is $60 from working hard. Therefore, the bank needs to charge an interest rate that makes the expected repayment from Pedro's working hard action equal to $100. Using this information, the interest rate would be:
Interest rate = ($100 - $60) / $100 = 40%.
i. Since Pedro's expected profit from farming while working hard is only $60, and he can earn $10 with certainty by not farming, it would not be rational for Pedro to take the loan. Pedro would not want the loan because his expected profit without farming is higher than the expected profit from farming while working hard.
j. A market failure occurs when the allocation of resources in a market is inefficient due to imperfections such as asymmetric information. In this case, the asymmetric information in credit markets, where the bank cannot observe Pedro's action, leads to a potential market failure. The bank needs to charge a higher interest rate (40%) to account for the possibility that Pedro might choose to be lazy, resulting in a lower expected profit from farming. This higher interest rate discourages Pedro from taking the loan, even though it could have been mutually beneficial for both Pedro and the bank. This information asymmetry creates inefficiencies in resource allocation and reduces the overall welfare in the credit market.