//moodle.tedu.edu.tr/pluginfile.php/57622/mod_resource/content/1/ECON421 HW2.pdf
ID: 1127765 • Letter: #
Question
//moodle.tedu.edu.tr/pluginfile.php/57622/mod_resource/content/1/ECON421 HW2.pdf k M Gmail H Hürriyet 2. (Two-period OLG Model) Consider a model with overlapping generations, in which N agents are born at each period t. Each period Ne increases at a constant rate n where Ne (1+n)N-1. Each agent is living two-periods. During the first period of their life, agents supply one unit of labor and in the second period they retire. At any time t young agents save se units of their labor income to consume in when they retire. The utility function of a generation t agent depends on consumption levels of two periods of their life, denoted by ce and de+1; and it is defined by: where denotes the discount factor. The production technology is Cobb-Douglas: K is the capital stoc I he quantity of labor. Capital depreciates fully in one period. ur is the wage level in period t, re the rate of return ocapital (b) Write down the household's problem and find Euler equation. (e) Characterize the savings function in terms of w and r+ corem to find partial derivative s in the interest rate? Diseuss your ontcome using the apExplanation / Answer
(a) The Budget Constraint is given by:
ct+1/(1+rt) . dt+1=(wtLt+rtKt)+1/(1+rt) . [w( t+1) L (t+1)+ r (t+1) K(t+1)]
(b) Household Problem:
Max U such that Budget Constraint given above in (a)
Max [u(ct)+ beta u(d t+1)] +LAMDAH [(wtLt+rtKt)+1/(1+rt) . {w( t+1) L (t+1)+ r (t+1) K(t+1)}- ct-1/(1+rt) . d(t+1)]
To solve we take the derivatives, dU/dct and dU/d d(t+1)
(c) Yt=ct +st
that is, st=Yt-ct
st=Kt^ alpha.Lt ^(1-alpha)-[wt .Lt + rt Kt+s(t-1)]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.