50% price discount on the new Ipad Pro to improve student online participation

INSTRUCTIONS: Similar to the problem sets, you must use this Microsoft Word document to answer the questions. After completing the exam, you must convert the document to PDF format and upload to Gradescope. You may use your notes, books and articles to answer the questions. You may send via email questions of clarification to Professor Boucher via Canvas.

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part i. TRUE OR FALSE

Please choose “TRUE” or “FALSE” in the box provided for each question.

1. The naïve ATE will be greater than the true ATE if .	TRUE ☐ FALSE X
2. In the Potential Outcome Framework, tells us what the average value of the outcome variable would have been for the control group if the control group had received the treatment.	TRUE ☐ FALSE X
3. When a monopolistic lender faces adverse selection, she will always charge the highest interest rate such that at least one type of borrower is willing to borrow.	TRUE ☐ https://studygroom.com/excellent-quick-approval-i-hope-to-work-for-you-again/FALSE X
4. Moral hazard exists in credit markets because lenders cannot https://studygroom.com/between-monetary-and-fiscal-policies-and-aggregate-demand-using-different-theories-variables-time-frame-methods-and-countries/observe some key borrower characteristics, such as how honest they are.	TRUE X FALSE ☐
5. A key feature of the design of a Randomized Control Trial is that the researchers allow individuals to choose (i.e., self-select) whether they are in the treatment group or the control group.	TRUE ☐ FALSE X
6. Informal Risk Sharing Arrangements are better suited to protect individuals against covariate shocks than idiosyncratic shocks.	TRUE ☐ FALSE X

Part II. Short Answers Questions.

Impact Evaluation [25 pts]. Due to the highly contagious Oso-21 virus, Development University moved all instruction on-line. Isaac, the President of Development University, was concerned that on-line instruction might reduce the quality of instruction. In order to address this issue, at the beginning of the semester, Isaac offered all students coupons for a 50% price discount on the new Ipad Pro. Isaac’s hypothesis was that the Ipad Pro would improve the quality of students’ participation in on-line classes and allow them to learn more.

At the end of the semester, Isaac hired Oscar, a distinguished professor of economics, to conduct an impact evaluation to test Isaac’s hypothesis. Oscar noticed that, although all students were offered the coupons, only half of them purchased an Ipad Pro. To conduct the impact evaluation, Oscar compared average semester GPA’s of students who purchased an Ipad Pro to those who didn’t

In the Potential Outcome Framework, is the outcome-with-treatment for individual. Write a sentence that clearly describes in the context of this study. Your answer should clearly define the treatment and the outcome variable in this study.

Let Y_1idenote the average semester GPA’s of students who purchased an Ipad Pro and let Y_0idenote the average semester GPA’s of students who did not purchase an Ipad Pro Further Let D_i Denote the GPA status for student i Note, D_iis a dummy variable. For each individual, we observe Y_i= Y_0i+ D_i (Y_1i− Y_0i), that is, we observe Y_1ifor those who used coupons to acquire Ipad and Y_0ifor those who did not purchase an Ipad pro.

. For each student, we observe Y_i= Y_0i+ D_i (Y_1i− Y_0i), that is, we observe Y_1ifor those who used coupons to acquire Ipad and Y_0ifor those who did not purchase an Ipad.

Write a sentence that clearly describes in the context of this study. Again, your answer should demonstrate that you have a clear understanding of both the treatment and the outcome variable in this study.

H_o A student who did not purchase an Ipad pro will have a higher GPA than a student who bought an Ipad pro.

H₁ Otherwise

In this context, The expectation that a student i did not purchase and Ipad pro and have his or her GPA higher than those who purchased an Ipad pro.; hence probability D_i=1

Let’s assume we have the following values for this study (some of these could be measured by Oscar while others could not):

Only two of the four values listed above were observable/measurable for the authors. Mark these two values in the table below:

i. X

ii. ☐

iii. ☐

iv. X

NOTE: For each of your answers in D-F, you should write down a number and indicate whether your answer is positive or negative. You may receive partial credit, so you may want to show the equation you use to generate your answer.

What is the value of the True Average Treatment Effect?

3.5-2.9= +0.6

What is the value of the Naïve Average Treatment Effect?

3.5-3.2= +0.3

What is the value of Selection Bias?

Provide a brief explanation of one potential cause of the selection bias that you found in part F. Your answer should demonstrate that you have a clear understanding of selection bias and what would cause it.

In this study, the study sample comprised of all the students thus not facing the problem of sampling bias. However there was a problem of time interval in that the study was terminated abruptly at the end of the semester. Chances are that some students might have been susceptible to other factors hindering them from using their Ipad pro. Moreover not all students purchased the Ipad pro. This means that the observations were biased, that is, the observations were not uniform. Hence the cause for large variance.

Information and Credit Markets [36 pts]. In the village of Green Pastures, 25% of the farmers are EXPERIENCED farmers and 75% are NEW farmers. Both types of farmers have zero wealth and need a loan of $100 in order to buy the inputs needed to farm. Both types of farmers have no way, other than farming, to earn income; so if they don’t farm, their income is zero. The only difference between EXPERIENCED and NEW farmers is as follows:

EXPERIENCED farmers have lots of experience and thus know how to protect their harvest against bad weather. An EXPERIENCED farmer always has a good harvest and earns revenue equal to $200.

NEW farmers have little experience and thus they don’t know how to protect their harvest against bad weather. With 60% probability a NEW farmer will have a good harvest and earn revenue equal to $200. With 40% probability, a NEW farmer will have harvest failure and earn revenue equal to $0.

Bilal is a moneylender who lives in Green Pastures. His opportunity cost of money is 0.2 (i.e., he would earn 20% interest if he put the money in a savings account instead of making a loan). Bilal offers limited liability loans, so a farmer does not have to repay the loan if he has harvest failure (zero revenues). Since Bilal lives in Green Pastures, he has perfect information about the farming experience of everybody in the village. This implies that he knows who is an EXPERIENCED farmer and who is a NEW farmer.

Partial credit may be awarded for all parts of this question, so you should write the initial equation used to setup your response in each part.

What is the highest interest rate an EXPERIENCED farmer would be willing to pay for a loan from Bilal?

A=P(1+rt); where P is the principal amount, r is percentage rate of interest and t is the period

A=100(r)

r= A/100

=(200-100)/100

=1%

What is the lowest interest rate Bilal would be willing to charge on a loan to an EXPERIENCED farmer?

<20%

What is the highest interest rate a NEW farmer would be willing to pay for a loan from Bilal?

0.6%

What is the lowest interest rate Bilal would be willing to charge on a loan to a NEW farmer?

<20%

For parts E – H, assume that Bilal is a monopolist.

What is the equilibrium interest rate Bilal would charge to an EXPERIENCED farmer?

100/200 x100 = 50%

How much expected profit does Bilal earn on a loan to an EXPERIENCED farmer?

100-$40

What is the equilibrium interest rate Bilal would charge to a NEW farmer?

0.4×0.6=0.24 =24%

How much expected profit does Bilal earn on a loan to a NEW farmer?

(24/100)x100 =$24

Now assume Bilal retires and no longer offers loans in the village. Nina is a loan officer from a bank in a nearby city. She is considering offering limited liability loans to farmers in Green Pastures. Just like Bilal, Nina’s opportunity cost of money is 0.2. Nina, however, does not know the farmers in Green Pastures so she cannot tell who is an EXPERIENCED farmer and who is a NEW farmer. All she knows is that 25% are EXPERIENCED and 75% are NEW farmers. As a result, she has to charge a single interest rate to everybody. For the rest of this problem, assume that the market for formal loans is described by perfect competition.

What type of asymmetric information problem does Nina face? Explain your answer in one or two sentences.

Nina is unaware that there is a probability 0.4 that 25% of her loan may not be recovered.

Write down an expression for , Nina’s expected profit from a loan, assuming that both EXPERIENCED and NEW types apply for a loan. Express this function as , where is the interest rate.

E () for all i_{j = A +Bi}

Will Nina be willing to offer loans to farmers in Green Pastures?

Yes

If yes, what interest rate will she charge and which type of farmer(s) will take the loans? If no, why can she not make loans in the village?

She will charge <20% on loans.

Only Experienced farmers will take the loan

RISK AND INSURANCE [21 pts]. Felipe must decide whether to farm or work as a construction worker. Farming is risky: 60% of the time farmers get a GOOD harvest and earn an income of $300, but 40% of the time they get a BAD harvest and earn an income of $0. Construction work, in contrast, is not risky. If Felipe chooses to be a construction worker, he earns a certain income of $160.

Felipe has initial wealth of $100 and his utility function is: , where C is consumption. (Remember that consumption is equal to initial wealth plus income.)

Partial credit may be awarded in this question, so you should show your initial equation.

What is the expected income of farming?

$100×0.6

$60=

What is Felipe’s certainty equivalent of farming?

$60+$0

=$60

What is Felipe’s risk premium of farming?

$60/$100

=60%

Which activity (farming or construction work) would Felipe choose?

Farming x

Construction work ☐

Now assume that an insurance agent comes to the village and offers sell an index insurance contract which is based on rainfall. The insurance premium (i.e., the cost of buying insurance) is $40. There are two possible values of rainfall, LOW and HIGH.

When rainfall is LOW, the insurance company makes a payout of $100 to the farmer. When rainfall is HIGH, the insurance company doesn’t pay the farmer anything.

Like most index insurance contracts, this one is not perfect. Sometimes a farmer has a BAD harvest even though rainfall is HIGH and sometimes a farmer has a GOOD harvest even though rainfall is LOW. This makes that there are four possible outcomes for a farmer. Their probabilities are as follows:

What is the expected income of an individual who buys insurance and farms? (Hint: The income of a farmer who buys insurance is equal to: Farm income – insurance premium + insurance payout).

Prob. Low rainfall= 0.3×0.1 =0.03 x$100 = $30

Insurance premium. = $30 insurance payout $40x 2 =$80

The income of a farmer = $300-110 = $190

Total costs = $30+$80 =$110

NB Probability high rainfall = no premium

Note that we now have three possible activities that Felipe can choose: 1) Farm without Insurance; 2) Farm and Buy Insurance; 3) Construction Work

Which activity will Felipe choose?

Farming without insurance x

Farming buying insurance ☐

Construction work ☐

Which activity will Eliana choose?

Farming without insurance x

Farming buying insurance ☐

Construction work ☐

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