% Exchange Rate Volatility with Capital
% Cameron Shelton and Jamus Lim

clear all;

% Calibration

alpha=0.3;	 	% Capital-labor share of production
tech=100;		% Technology parameter
H1=100;			% Money supply country 1
H2=100;			% Money supply country 2
N=30;			% Number of agents in each country in each generation
T=500;			% Number of periods
w1=100;			% Initial wages in country 1
w2=100;			% Initial wages in country 2
pix=0.3;		% Propensity to experiment
a=0.25;			% Probability of experimenting on savings-consumption
b=0.25;			% Probability of experimenting on capital-currency
c=0.25;			% Probability of experimenting on currency-country

% Matrices of Variables

W1=zeros(1,T);	       % Wages of country 1
W2=zeros(1,T);	       % Wages of country 2
P1=zeros(1,T);	       % Prices of country 1
P2=zeros(1,T);	       % Prices of country 2
e=zeros(1,T);	       % Exchange Rate
r1=zeros(1,T);	       % Rental rate of country 1
r2=zeros(1,T);	       % Rental rate of country 2
K1=zeros(1,T);	       % Capital stock of country 1
K2=zeros(1,T);	       % Capital stock of country 2
S1=zeros(1,T);	       % Real value in monetary holdings of currency 1
S2=zeros(1,T);	       % Real value in monetary holdings of currency 2
M1=zeros(N,T);	       % Nominal currency holdings of currency 1
M2=zeros(N,T);	       % Nominal currency holdings of currency 2
k11=zeros(N,T);	       % Real capital investments of citizens 1 in country 1
k12=zeros(N,T);	       % Real capital investments of citizens 1 in country 2
k21=zeros(N,T);	       % Real capital investments of citizens 2 in country 1
k22=zeros(N,T);	       % Real capital investments of citizens 2 in country 2
s11=zeros(N,T);        % Real value of investments in citizens 1 in currency 1
s12=zeros(N,T);        % Real value of investments in citizens 1 in currency 2
s21=zeros(N,T);        % Real value of investments in citizens 2 in currency 1
s22=zeros(N,T);        % Real value of investments in citizens 2 in currency 2
C1young=zeros(N,T);    % Consumption of country 1 for young
C1old=zeros(N,T);      % Consumption of country 1 for old
C2young=zeros(N,T);    % Consumption of country 2 for young
C2old=zeros(N,T);      % Consumption of country 2 for old
U1=zeros(N,T);	       % Utility of citizens in country 1
U2=zeros(N,T);	       % Utility of citizens in country 2
F1=zeros(N,T);	       % Fitness of strategies in country 1
F2=zeros(N,T);	       % Fitness of strategies in country 2
UU1=zeros(N,1);	       % Experimental utility of citizens in country 1
UU2=zeros(N,1);	       % Experimental utility of citizens in country 2
FF1=zeros(N,1);	       % Experimental fitness of strategies in country 1
FF2=zeros(N,1);	       % Experimental fitness of strategies in country 2

% Strategy choices

A1=rand(N,T+1);	% Saving-consumption choice for country 1
A2=rand(N,T+1);	% Saving-consumption choice for country 2
B1=rand(N,T+1);	% Currency-capital choice for country 1
B2=rand(N,T+1);	% Currency-capital choice for country 2
C1=rand(N,T+1);	% Currency-country choice for country 1
C2=rand(N,T+1);	% Currency-country choice for country 2
D1=rand(N,T+1);	% Capital-country choice for country 1
D2=rand(N,T+1);	% Capital-country choice for country 2

% Experimental strategy choices

E1=zeros(N,4);	% Experimental strategies for country 1
E2=zeros(N,4);	% Experimental strategies for country 2

% Equations

% C(j,i,t)(t+1) = M1(t)/P1(t+1) + M2(t)/P2(t+1) + R1(t+1)k1(j,i,t)(t+1) + R2(t+1)k2(j,i,t)(t+1)	      Consumption when old
% C(j,i,t)(t) = W(t) - M1(t)/P1(t) - M2(t)/P2(t) - k1(j,i,t)(t+1) - k2(j,i,t)(t+1)		      Consumption when young
% N*w(t) - K1(t+1) - K2(t+1) = H1(t)/P1(t) + H2(t)*e(t)/P2(t)	     				      Money market equilibrium
% tech*alpha*K(j,t)^(alpha-1) = r(j,t)				     				      Marginal product of capital
% tech*K(j,t)^alpha - tech*K(j,t)*alpha*K(j,t)^(alpha-1) = W(j,t)				      Marginal product of labor

% Initial values

W1(1,1)=w1;
W2(1,1)=w2;

for i=1:N
	k11(i,2)=W1(1,1)/N*A1(i,1)*(1-B1(i,1))*(D1(i,1));
	k21(i,2)=W2(1,1)/N*A2(i,1)*(1-B2(i,1))*(D2(i,1));
	k12(i,2)=W1(1,1)/N*A1(i,1)*(1-B1(i,1))*(1-D1(i,1));
	k22(i,2)=W2(1,1)/N*A2(i,1)*(1-B2(i,1))*(1-D2(i,1));
end
K1(1,2)=sum(k11(:,2),1)+sum(k21(:,2),1);
K2(1,2)=sum(k12(:,2),1)+sum(k22(:,2),1);
for i=1:N
	s11(i,1)=W1(1,1)/N*A1(i,1)*(B1(i,1))*(C1(i,1));
	s21(i,1)=W2(1,1)/N*A2(i,1)*(B2(i,1))*(C2(i,1));
	s12(i,1)=W1(1,1)/N*A1(i,1)*(B1(i,1))*(1-C1(i,1));	% Line 100
	s22(i,1)=W2(1,1)/N*A2(i,1)*(B2(i,1))*(1-C2(i,1));
end
S1(1,1)= sum(s11(:,1),1)+sum(s21(:,1),1);
S2(1,1)= sum(s12(:,1),1)+sum(s22(:,1),1);
P1(1,1)=H1/S1(1,1);
P2(1,1)=H2/S2(1,1);	
e(1,1)=P1(1,1)/P2(1,1);
for i=1:N
	C1young(i,1)=W1(1,1)/N*(1-A1(i,1));
	C2young(i,1)=W2(1,1)/N*(1-A2(i,1));
end

% Portfolio allocation decisions for capital

for t=2:T

	for i=1:N
		k11(i,t)=W1(1,t-1)/N*A1(i,t-1)*(1-B1(i,t-1))*(D1(i,t-1));
		k21(i,t)=W2(1,t-1)/N*A2(i,t-1)*(1-B2(i,t-1))*(D2(i,t-1));
		k12(i,t)=W1(1,t-1)/N*A1(i,t-1)*(1-B1(i,t-1))*(1-D1(i,t-1));
		k22(i,t)=W2(1,t-1)/N*A2(i,t-1)*(1-B2(i,t-1))*(1-D2(i,t-1));
	end

	K1(1,t)=sum(k11(:,t),1)+sum(k21(:,t),1);	% Capital of country 1 at time t
	K2(1,t)=sum(k12(:,t),1)+sum(k22(:,t),1);	% Capital of country 2 at time t

% Marginal products of capital and labor

	r1(1,t)=tech*alpha*K1(1,t)^(alpha-1);
	r2(1,t)=tech*alpha*K2(1,t)^(alpha-1);
	W1(1,t)=tech*K1(1,t)^(alpha) - tech*K1(1,t)*alpha*K1(1,t)^(alpha-1);
	W2(1,t)=tech*K2(1,t)^(alpha) - tech*K2(1,t)*alpha*K2(1,t)^(alpha-1);

% Portfolio allocation decisions for currency

	for i=1:N
		s11(i,t)=W1(1,t)/N*A1(i,t)*(B1(i,t))*(C1(i,t));
		s21(i,t)=W2(1,t)/N*A2(i,t)*(B2(i,t))*(C2(i,t));
		s12(i,t)=W1(1,t)/N*A1(i,t)*(B1(i,t))*(1-C1(i,t));
		s22(i,t)=W2(1,t)/N*A2(i,t)*(B2(i,t))*(1-C2(i,t));
	end

	S1(1,t)= sum(s11(:,t),1)+sum(s21(:,t),1);	% Real savings of currency 1 at time t
	S2(1,t)= sum(s12(:,t),1)+sum(s22(:,t),1);	% Real savings of currency 2 at time t


% Prices

	P1(1,t)=H1/S1(1,t);
	P2(1,t)=H2/S2(1,t);	

	e(1,t)=P1(1,t)/P2(1,t);

% Consumption and utility

	for i=1:N
		C1young(i,t)=W1(1,t)/N*(1-A1(i,t));
		C2young(i,t)=W2(1,t)/N*(1-A2(i,t));
		C1old(i,t)=s11(i,t-1)*P1(1,t-1)/P1(1,t) + s12(i,t-1)*P2(1,t-1)/P2(1,t) + k11(i,t)*r1(1,t) + k12(i,t)*r2(1,t);
		C2old(i,t)=s21(i,t-1)*P1(1,t-1)/P1(1,t) + s22(i,t-1)*P2(1,t-1)/P2(1,t) + k21(i,t)*r1(1,t) + k22(i,t)*r2(1,t);
      
      U1(i,t-1)=log(C1young(i,t-1)) + log(C1old(i,t));
		U2(i,t-1)=log(C2young(i,t-1)) + log(C2old(i,t));
	end

% Genetic algorithms

% Imitation operator

	F1(:,t-1)=U1(:,t-1)/sum(U1(:,t-1));	% Fitness of strategies of generation t-1 in country 1
	F2(:,t-1)=U2(:,t-1)/sum(U2(:,t-1));	% Fitness of strategies of generation t-1 in country 2

	for i=1:N

		x1=rand;
		y1=0;
		counter=0;

		while x1 > counter
			y1=y1+1;
			counter=sum(F1(1:y1,t-1));
		end
	
		A1(i,t+1)=A1(y1,t-1);
		B1(i,t+1)=B1(y1,t-1);
		C1(i,t+1)=C1(y1,t-1);
		D1(i,t+1)=D1(y1,t-1);

		x2=rand;
		y2=0;
		counter=0;

		while x2 > counter
			y2=y2+1;
			counter=sum(F2(1:y2,t-1));
		end
	
		A2(i,t+1)=A2(y2,t-1);
		B2(i,t+1)=B2(y2,t-1);
		C2(i,t+1)=C2(y2,t-1);
		D2(i,t+1)=D2(y2,t-1);	% Line 200
	end

% Experimentation operator

	E1(:,1)=A1(:,t-1);
	E1(:,2)=B1(:,t-1);
	E1(:,3)=C1(:,t-1);
	E1(:,4)=D1(:,t-1);
	E2(:,1)=A2(:,t-1);
	E2(:,2)=B2(:,t-1);
	E2(:,3)=C2(:,t-1);
	E2(:,4)=D2(:,t-1);

	for i=1:N
	
		z1=rand;		% whether to experiment
		if z1 < pix
			q1=rand;	% which portfolio choice to experiment
			v1=rand;	% experimental value
			if q1<a
				E1(i,1)=v1;
			else if q1<a+b
				E1(i,2)=v1;
			else if q1<a+b+c
				E1(i,3)=v1;
			else
            E1(i,4)=v1;
         end
      end
      
		z2=rand;		% whether to experiment
		if z2 < pix
			q2=rand;	% which portfolio choice to experiment
			v2=rand;	% experimental value
			if q2<a
				E2(i,1)=v2;
			elseif q2<a+b
				E2(i,2)=v2;
			elseif q2<a+b+c
				E2(i,3)=v2;
			else
            E2(i,4)=v2;
         end
      end
   end
   
% Election operator

	for i=1:N
      
   	ss11(i,1)=W1(1,t-1)/N*E1(i,1)*(E1(i,2))*(E1(i,3));
		ss21(i,1)=W2(1,t-1)/N*E2(i,1)*(E2(i,2))*(E2(i,3));
		ss12(i,1)=W1(1,t-1)/N*E1(i,1)*(E1(i,2))*(1-E1(i,3));
		ss22(i,1)=W2(1,t-1)/N*E2(i,1)*(E2(i,2))*(1-E2(i,3));
		SS1(1,1)= sum(ss11(:,1),1)+sum(ss21(:,1),1);
		SS2(1,1)= sum(ss12(:,1),1)+sum(ss22(:,1),1);
      
	kk11(i,1)=W1(1,t-1)/N*E1(i,1)*(1-E1(i,2))*(E1(i,4));
		kk21(i,1)=W2(1,t-1)/N*E2(i,1)*(1-E2(i,2))*(E2(i,4));
		kk12(i,1)=W1(1,t-1)/N*E1(i,1)*(1-E1(i,2))*(1-E1(i,4));
		kk22(i,1)=W2(1,t-1)/N*E2(i,1)*(1-E2(i,2))*(1-E2(i,4));
		KK1(1,1)=sum(kk11(:,1),1)+sum(kk21(:,1),1);
		KK2(1,1)=sum(kk12(:,1),1)+sum(kk22(:,1),1);

      CC1young(i,1)=W1(1,t-1)/N*(1-E1(i,1));
		CC2young(i,1)=W2(1,t-1)/N*(1-E2(i,1));
		CC1old(i,1)=ss11(i,1)*P1(1,t-1)/P1(1,t) + ss12(i,1)*P2(1,t-1)/P2(1,t) + kk11(i,1)*r1(1,t) + kk12(i,1)*r2(1,t);
		CC2old(i,1)=ss21(i,1)*P1(1,t-1)/P1(1,t) +	ss22(i,1)*P2(1,t-1)/P2(1,t) + kk21(i,1)*r1(1,t) + kk22(i,1)*r2(1,t);
		UU1(i,1)=log(CC1young(i,1)) + log(CC1old(i,1));
		UU2(i,1)=log(CC2young(i,1)) + log(CC2old(i,1));

      if UU1(i,1)>=U1(i,t-1)
         A1(i,t+1)=E1(i,1);
         B1(i,t+1)=E1(i,2);
         C1(i,t+1)=E1(i,3);
         D1(i,t+1)=E1(i,4);
      end
      if UU2(i,1)>=U2(i,t-1)
         A2(i,t+1)=E2(i,1);
         B2(i,t+1)=E2(i,2);
         C2(i,t+1)=E2(i,3);
         D2(i,t+1)=E2(i,4);
      end
   end
end
end
end

time=1:T;

% Graph exchange rate

subplot(2,2,1), plot(time,e,'k');
xlabel('Time');
ylabel('Exchange Rate');
legend('Exchange Rate');
figure(gcf);

% Graph real interest rate

subplot(2,2,2), plot(time,r1,'b',time,r2,'r');
xlabel('Time');
ylabel('Real Interest Rate');
legend('Interest Rate 1','Interest Rate 2');
figure(gcf);

% Graph capital

subplot(2,2,3), plot(time,K1,'b',time,K2,'r');
xlabel('Time');
ylabel('Capital');
legend('Capital 1','Capital 2');
figure(gcf);

% Graph wages

subplot(2,2,4), plot(time,W1,'b',time,W2,'r');
xlabel('Time');
ylabel('Wages');
legend('Wages 1','Wages 2');
figure(gcf);