# program equilibrium
#This program solves the model described in 
#"On the Needed Quantity of Government Debt"
#Federal Reserve Bank of Minneapolis Working Paper 648
#by Kathryn Birkeland and Edward Prescott

#Input file:  equilibrium.inp
#Output file: equilibrium.out
#See Appendix A in the paper and readme.txt for more information

#Inputs:		AR			=	retirement age less 20 years
#								(note: the agent is born at t=0 and age=20)
#				AD			=	lifespan less 20 years
#				gamma		=	growth rate of technology
#              	eta     	=   growth rate of the population
#				irate		=	interest rate
#				theta		=	capital share in the cobb-douglas production function
#				delta		=	depreciation rate of the capital stock
#				alpha		=	preference parameter 
#				Z			= 	labor-augmenting technology in production # #  
#              	beta   		 =	time discount factor of the household
#              	Npop   		 =   size of the initial population
#				tauh		=	input labor income tax rate
#				tauk		=	input tax rate on net capital income
#				g			=	growth rate of aggregate output
#				Ncohort		 =	size of the cohort entering the workforce in period 1
#				Nwork		=	size of the working population in period 1	
#				r			=	rental price of capital
#				HK			=	aggregate capital labor ratio
#				w			=	wage rate
#				CH			=	aggregate consumption to labor ratio
#				cw		=	consumption of an individual
#				hi		=	individual labor supply
#				H		=	aggregate labor supply
#				C		=	aggregate consumption
#				K		=	aggregate capital stock
#				Y		=	aggregate output
#				X		=   aggregate investment

#				utility		=	lifetime utility of a person entering the workforce in t=1
#							utility/discount can be used for the welfare comparison
#							in terms of lifetime consumption equivalents 
#
#Written by Kathryn Birkeland and Edward C. Prescott 3-24-06
#Revised KFB 12-28-06
#Modified by B. Goff for classroom use;  making for y fitting long term growth 
#rather than steady state


nulldata 100
          
    series e = normal()  
    series gamma = 0.02 + .005*e

	scalar eta=0.03
	scalar irate = 0.04
	scalar theta = 0.35
	scalar delta = 0.05
	scalar alpha = 2.14626
	scalar Z = 0.026888
	scalar beta = 0.980768
	
	scalar tauh = 0.4
	scalar tauk = 0.2
	
	scalar dep = 0.175
	scalar ARet = 45
	scalar AD = 65
    series t = time 

#growth rate of per capita consumption
genr g = (1+gamma)*(1+eta)-1   

smpl 1 1 
series Npop = 100
smpl 2 100
series Npop = (1+eta)*Npop(-1)

smpl 1 100

#Compute the size of the cohort born in period one given the initial population

series xeta = 0
   loop i=1..AD
   series xeta = xeta + (1/(1+eta))^i
   endloop 
   
#This is a simplification of Prescott 
genr Ncohort   = Npop

#Find the size of the working population given the size of cohort one
series xwork=0
   loop i=1..ARet
    series xwork = xwork + (1/(1+eta))^i
    endloop 
     
genr Nwork = Npop 

#Compute the rental rate on capital, capital labor ratio, and wage
genr r = irate/(1-tauk)+delta
genr HK    = ((r/theta)^(1/(1-theta)))/Z
genr w 	= Z^(1-theta)*(1-theta)*(HK)^(-theta)
genr KH	= 1/HK

#Compute individual consumption and labor 
genr CH	= Z^(1-theta)*KH^theta - (g+delta)*KH
genr cw = 1/(alpha/((1-tauh)*w) + Npop/(CH*Nwork))
genr hi	= 1 - alpha*cw/(w*(1-tauh))

#Compute aggregate labor, consumption, capital, output and investment
genr H = Nwork*hi
genr Ci = Npop*cw
genr K = KH*H
genr Y= (K^theta)*(Z*H)^(1-theta)
      	genr X = Y-Ci
          genr Ypc = (Y-Y(-1))/Y(-1) 
             genr Ypercap = Y/Npop