Quiz 2 EC3339 1.9) prod 9 ;= 3 un prod y = 2 asy invest / borrow > ai or y lend > R Hint: R> 9 R>y pv will lend u npr will lend Pr will borr unpr will borr Rey R<d K>2 + RS 3+ V > + Ris 2 or 3 y < << a pr borr to recieve a - no limit un lend to recieve k - limited X 9 < Ray 3 can't be <2 × y <R = a R= 3 pr borr to recieve a - limited un lend to recieve k - limited unproductive entrepeneur lends I unit to recieve 3 unit in period2 ( lends entire net worth ) productive entrepeneuris indifferent. borrows due to market supply of lenders. borrows/ invests I unit to recieve 3 unit in period 2
* unable to use Lagrangian throughout! sizo Mizo I.b) Ci=10g(w+-0.85-P+xi)+0.85log(4-8)1.8+(h+++1)xi -(1.03)1]+ A+[0.1(4-8) 1.85+0.(h+P+1) 4 -(1.03)1]+ MAX! ci +x] = = ' + b; RI y2=q‘x; too many unknowns ? c} = 2| +bà -xi c2 = y2 - bj RI C1 =2,+b= = X, RI C1 185 + 1 - 1 Ca = y2 -b? C2 : 2-1 3 prcz PC = 0 84 5 070 un = 0.75 zi + b2 -xi RI y= 2 R1=3 2 ;= 1.85 b2 =1 q'= 3 ( productive entrepeneur y? = d'x1 2 = 3x! borrows lunit to recieve 3) } =x? Possible investment choices : 2-1 1. investing based on y= = q'x ; - > C2 = 0.66 = 1.85+ - 2 2. investing Jun it S i ( = 0 . 6 59 340 ... ) that was born wed Ci 3. investing I borro wed unit + net worth of 1.85 . = 0.85 = 2-1 1.85 +1- 1 ( 20. 845070 ... ) ?= = 1.5=2 2-1 1.85+1-2.85
[. c) sf 20 nº 20 [+=10g(w+-1-Prx) +0.85 log [(4-8)} +(h+1 +1)x; - (1.03)0]+1}[0.1 ( 4-8)} +0.1 (h++++++) x+-(1.03)0]+ M+x+ & - yk-b! RI zi + b2 -xi too many unknowns ? y= = 2 k,=3 2; = 1 b2 = 0 q'= 3 (unproductive entrepeneur is lending not borrowing ) y= a'xi 2 = 3x0 = = ? xi= oro? CR = 12 2-0 = 2 ci 1+2 - 0 x =0 (unproductive entrepeneur is lending not inverting