statistic question

User Generated

znttvrznttvr

Mathematics

Description

The question is separated into two parts. Please help me finish all parts. Statistic question. The detailed information need to log into my school account to see the full parts.

Unformatted Attachment Preview

Problem set #4 This assignment goes through the model of informal insurance, and credit markets with limited liability and moral hazard (lecture notes “Credit”). A suggestion: If I were in your position, before I work on this assignment I would look at the slides titled “Credit” and work through each model on paper, making sure you understand the meaning of each step. After you are done with that, you should try this assignment without help. If you get stuck, look again at the lecture notes. Part A: Informal Insurance (10 points) The table below shows the average production among three farmers in Oommo Nadda, a village in rural Ethiopia. On average, production among these three farmers is 50 quintals per year. The table below shows production this year. Assume that the three farmers have a full risk sharing agreement that includes only themselves. Fill out the table with the appropriate numbers. Name of farmers Average harvest among three farmers Harvest for each person this year Rashid 50 83 Ahmed 50 52 Ibrahim 50 45 Amount consumed (after informal insurance) Idiosyncratic shock Aggregate shock Part B: Formal Insurance Binti is a Kenyan farmer who plants her land with maize. In a good year, Binti gets 2 tons of maize. In a bad year, she gets only 0.8 tons of maize. In both cases she sells her maize for $1,500 per ton. The likelihood of a good harvest is 80%. Her utility from consumption c is given by u(c) = √c, and assume that consumption is equal to her farm income. In what follows, round to two decimal places. a. What is the value of Binti’s two ex-post utilities? b. What is the value of Binti’s ex-ante (a.k.a. expected) utility? c. What is the value of Binti’s expected income? d. Suppose that Binti is fully insured. Write down her (1) income after paying premium π in a good year, (2) income after paying premium π and receiving the payout V in a bad year, (3) calculate the value of the payout. e. Write down the expected profit function of the insurance company. f. In a perfectly competitive market, expected profits are equal to zero. Set the equation E(∏)=0, plug V from part d, and solve for the premium π. Part C: Credit markets (introduction) This is the first part of an assignment which will be completed in problem set 4. Consider the problem of an entrepreneur/borrower with no money and illiquid assets valued at C= $50 and a project requiring L=200 to be carried out. Assume that the borrower cannot use his illiquid assets to finance the project. The entrepreneur Once the entrepreneur undertakes the project, she decides either to work hard or to shirk. • • If she works hard, then she earns a high return R=$500 with probability p=0.75 and earns nothing with probability (1-p)=0.25. If she shirks, she earns a high return with probability q=0.25 and earns nothing with probability (1-q)=0.75. The borrower has ex-post utility u(y)=y-D if she works hard and u(y)=y if she does not work hard, where y is her income (after loan payments) earned from the project. Assume D=125. The bank: A bank is willing to finance the project and lend $200 to the borrower. The bank charges the agent an interest rate of i on the loan. The borrower always repays the loan when she succeeds. If she fails, she is protected by limited liability: she repays nothing to the bank. Finally, assume that the bank could also purchase $200 in risk-free bonds with a return of r=0.10, and that the financial markets are perfectly competitive. Section A1: No collateral 1. The borrower Suppose the borrower takes a loan of $200 from the bank. Suppose that the interest rate charged on the loan is i (we'll find i later). (HINT: Slides 15-23) a. What is her ex post income yfail if she fails? NOTE: I'm asking for realized income, NOT utility! b. What is her ex post income ysucceed if she succeeds? (hint: this will be a function of the interest i). c. Calculate her Expected Utility EUwork if she works hard. (hint: this will be a function of the interest i). d. Calculate her Expected Utility EUshirks if she shirks. (hint: this will be a function of the interest i). e. Write down the condition under which the borrower will work hard. f. No-shirking condition: Manipulating the condition you found in e, find the maximum i for which the borrower is going to work hard. Call this interest i*1. NOTE: i*1 will be a number.
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

It...


Anonymous
Just what I needed. Studypool is a lifesaver!

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags