isical.ac.in JRF Quantitative Economics Sample Questions for ISI Admission Test : Indian Statistical Institute
Name of the University : Indian Statistical Institute
Exam : ISI Admission Test
Document Type : Sample/Previous Year Question Paper
Name of the Subject : Quantitative Economics
Year : 2016
Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-Jrf-QE.html
Download Sample/Previous Years’ Questions :
QEA 2016 : https://www.pdfquestion.in/uploads/11360-JRF-QEA-2016.pdf
QEB 2016 : https://www.pdfquestion.in/uploads/11360-JRF-QEB-2016.pdf
QEA 2015 : https://www.pdfquestion.in/uploads/11360-JRF-QEA-2015.pdf
QEB 2015 : https://www.pdfquestion.in/uploads/11360-JRF-QEB-2015.pdf
QEA 2014 : https://www.pdfquestion.in/uploads/11360-JRF-QEA-2014.pdf
QEB 2014 : https://www.pdfquestion.in/uploads/11360-JRF-QEB-2014.pdf
JRF Quantitative Economics Sample Questions for ISI Admission Test :
Test Code: QEB
Session : Afternoon
Questions : 10
Time : 2 hours
** On the answer booklet write your Name, Registration number, Test Code, Number of the booklet etc. in the appropriate places.
Related : Indian Statistical Institute JRF Mathematics ISI Admission Test Sample Question Paper : www.pdfquestion.in/11356.html
** This test has 10 questions. Answer any 4.
** All questions carry equal marks (25).
1. Consider a market consisting of 600 buyers and 400 sellers of used cars. There are 100 bad quality used cars (lemons) and 300 good quality used cars (peaches). Suppose the valuation of a lemon is 20 for both a buyer and a seller. The valuation of a peach, however, is 100 for a buyer and 60 for a seller.
(a) What is the ancient outcome?
(b) Solve for the market outcome when the identity of all cars, i.e. whether a car is lemon or a peach, is common knowledge. Illustrate the outcome graphically.
(c) Next, suppose that the identity of any car is private knowledge of its owner. What is the market outcome? Illustrate the outcome graphically.
(d) Suppose any lemon owner, at a cost of 10, can transform a lemon into a peach. Will she have an incentive to do that? Explain. [5+5+10+5=25]
2. (a) Consider a farmer who can pump groundwater from an aquifer beneath his land to which no one else has access. The prot from water pumped to the surface is f(X) – cX where X is the number of litres of diesel used for pumping water,
(a) Characterize the prot-maximizing value of X
(b) Now suppose the number of farmers in the area with access to the aquifer who could also pump water from it is effectively unlimited. The prot for farmer i is now given by where xi is the diesel used by farmer i and X is the total litres of diesel used by all farmers who pump water. Characterize the total prot and the total litres of diesel that will be used, assuming that each farmer tries to maximize his own prot. Are the total prot and the total diesel used larger or smaller or the same as in the case of a single farmer in the previous part? Why?(c) Now suppose the number of farmers who can pump water from the aquifer is a xed nite number N.
(c) Characterize the litres of diesel that will be used by each of the N farmers. Is the total prot of all farmers larger or smaller or the same as the corresponding values in the previous two cases? Why? [5+10+10=25]
3. Suppose agents need to borrow to invest in a project.There are two types of borrowers, risky and safe, characterised by the probability of success of their projects, pr and ps respectively, where 0 < pr < ps < 1: Risky and safe borrowers exist in proportions – and 1 ?? in the population. Suppose a risky investment project equires one unit of capital.The outcome of the project is either a success (S) or failure (F).
The return of a project of a borrower of type i is Ri > 0 if successful and 0 if it fails. Assume that risky and safe projects have the same mean return, that is, prRr = psRs R ; but risky projects have a greater spread around the mean. Borrowers are isk-neutral and maximise expected returns. Borrowers of both types have an reservation pay to you:
(i) Write down the expressions for expected prots of the bank from each type of borrower.
(ii) Write down the expressions for expected payos to each type of borrower.
(iii) Given the zero-prot constraint on each loan, what repayment (principal plus interest), ri; i = r; s; will the bank oer to type i borrower? Will the type i borrower accept this oer? Give clear explanations for your answers.
(iv) What will be the average repayment rate (rate at which the bank gets repaid)?