Question

Exercise 2. Market Demand for Student Loans (Non-Linear) Studenti has no income today (my=0), but expects to make 100 tomorrow (m2; = 100). Her utility between consumption today, Ch, and consumption tomorrow, C2,1, is yn = C1,C2,1. Although without income endowment today, student i can borrow at a market interest rate, r. The maximum she can borrow for consumption today is cu =(m2,- €2)/(1+r). a) Consider b, as the quantity borrowed today (b=cu) and p as the price of borrowing (p=1+r). What is studenti's demand for loans b (p)? b) Suppose there are n=2,100 students with identical present and future endowments and preferences between present and future consumption. What is the market demand for loans? c) If the market interest rate for loans to students is r-5%, how much borrowing will the market demand?

Answer 1

Exercise 2 Given informations, m , ;=0 or income in Remiad 1=0. and mzi= 100 or " " Period 2=6100 (expected) also, Gli and Cze be the consumptions of today and tomorro Her utility Ui=C i Czi Although without income endowment today student i can borrow at a market in ter est rate, r. her constraint so, she has has of in consumption period 1 (mzi-C2i) - Cil= tr Her @ Peso borrowing in period 1 = bid = Cic. and P = 1tr Henee, to find student's demand for loans, we have to maximize her utility subject to the budget constraint. (mzi - C2i) Hence, Mose u= bi Cac sub to bi => Itr Now, from, biz 100 - Cai to =D C2i = 100- biCitro).... from, we bi Cao = bi 8100 - bì (ltr)] [ from 1 as a ix maximized for be, then, Now, od u =0 dbi d. = D biz 100- bi (1+r) = 0 =D 100 - 2bi (ltr) = 0 Itr for loans bibp demand Hence, students is

- Page 2) students, with identical present preferences, then market demand Now, if there are n=2100 and future endowments and for loons, B, GP) = nx běCP) =DB(P) = 21000 [B(A) = market demand Say] - Ž bilp)] 105 000 BCP= 10000 manket demand for lomos. @ If market rate of interest, r= 56, then, p = 1 + 0.05 - 1:05. 105000 100000 Hence, Market demand =B (1005)=- 1.05 The market demand for loans = 100000 you my friend. ☺ solution is clear to Hope the