hhfair.gms : Household Optimization Problem by Fair

**Description**

This is a theoretical optimizing model of a typical household. a detailed description can be found in Chapter 3 of Ray Fair's book.

**Reference**

- Fair, R C, Specification, Estimation, and Analysis of Macroeconomic Models. Harvard University Press, Cambridge, Mass, 1984.

**Small Model of Type :** NLP

**Category :** GAMS Model library

**Main file :** hhfair.gms

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$Title Household Optimization Model by Fair (HHFAIR,SEQ=69)
$Ontext
This is a theoretical optimizing model of a typical household.
a detailed description can be found in Chapter 3 of Ray Fair's book.
Fair, R, Specification, Estimation, and Analysis of Macroeconomic
Models. Harvard University Press, Cambridge, Mass, 1984.
$Offtext
Sets tl long time horizon / 0, 1, 2, 3 /
t(tl) optimizing horizon / 1, 2, 3 /
tt(t) terminal year / 3 /
Scalars
p price of goods / 1.0 /
r one period interest rate / .07 /
tr transfer payment / 0 /
th total number of hours in the period / 1004.72366 /
w wage rate / 1.0 /
d income tax rate / .2 /
a1 distribution coefficient in ces function / .5 /
a2 elasticity coefficient in ces function / -.5 /
am terminal assets target / 1100 /
lambda discount rate / .944 /
lstar maximum labor available in each time period / 400 /
gamma1 coefficient 1 in money holding function / .255905/
gamma2 coefficient 2 in money holding function / 1.0 /
Parameter ufact(t) utility function factor ;
ufact(t) = power(lambda,ord(t)-1) ; Display ufact;
Variables
a(tl) assets
c(t) consumption
l(t) labor supplied
m(tl) money holdings
n(t) time spent on money holdings
obj objective function value
s(tl) savings
tax(t) net taxes paid
u(t) utility
y(t) income
Equations
objective objective function
utility(t) utility in each period
income(t) before tax income
taxes(t) net taxes
savings(t) savings
budget(tl) budget constraint
timemoney(t) time spent taking care of money holdings
terminal(t) terminal condition for assets
dom1(t) domain constraint on timemoney equation
dom2(t) domain constraint on utility equation ;
objective.. obj =e= prod(t, u(t)**ufact(t)) ;
utility(t)..
u(t) =e= (a1*c(t)**(-a2) + (1-a1)*(th-l(t)-n(t))**(-a2))**(-1/a2)/100 ;
income(t).. y(t) =e= w*l(t) + r*a(t) ;
taxes(t).. tax(t) =e= d*y(t) - tr;
savings(t).. s(t) =e= y(t) - tax(t) - p*c(t) ;
budget(tl-1).. s(tl) =e= a(tl) - a(tl-1) + m(tl) - m(tl-1) ;
timemoney(t).. n(t)*(m(t) - gamma1*p*c(t)) =e= gamma2 ;
terminal(tt).. a(tt) + m(tt) =e= am ;
dom1(t).. m(t) =g= 1.01*gamma1*p*c(t) ;
dom2(t).. l(t) + n(t) =l= .9*th ;
Model hh household optimization model / all / ;
l.up(t) = lstar; a.fx("0") = 1000; m.fx("0") = 100;
c.lo(t) = 100; l.lo(t) = 100; u.lo(t) = .01;
a.l(t) = 1000; m.l(t) = 100; l.l(t) = 400; u.l(t) = 1;
Solve hh maximizing obj using nlp;
```