# R SCRIPT FILE FOR ANALYSING THE GG AND AA CURVES
#
# SET INITIAL VALUES OF THE GROWTH PARAMETERS
#
 hatm <- 0.14
 delta <- 0.05
 varpi <- .015
 alpha <- 20             # long-run adjustment cost parameter
 sralpha <- 100          # short-run adjustment cost version of alpha
 gamma <- .2
 newgamma <- .1822857    # reflecting improvement in resource allocation
 tau <- .01
 oplkr <- .03
 newoplkr <- .0312
 Ups <- .2
 inf <- .02              # inflation rate
#
#
# SET VALUES OF VARIABLES OBTAINED FROM GGAAssg.R  --- saved in GGAAssg.xls
#
 g <- 0.01405           # original values obtained with 2% inflation
 r <- 0.03961631
 L <- 0.02671
 newg <- .01482000      # new values after the efficiency improvement
 newr <- .04041088
 newL <- .02775
# Yf <- .06193458       # changes in full-employment output from 
# newYf <- .06441026    #   efficiency improvement
#
# CALCULATE THE VALUES OF lambda and varphi
# 
 varphi <- sqrt((1 - Ups)*3/oplkr)         # recalculate these here 
 lambda <- varphi/oplkr                    #  rather than copy them 
 newvarphi <- sqrt((1 - Ups)*3/newoplkr)   #  from  GGAAssg.xls
 newlambda <- newvarphi/newoplkr
#
# CALCULATE mterm, acterm, tterm and dmterm FOR OPTIMUM LIQUIDITY/CAPITAL 
#   RATIO
#
# Initially set KU = 1
#
 KU <- 1
#
 mterm <- hatm * (1 - gamma) - delta 
 newmterm <- hatm * (1 - newgamma) - delta    # mterm modified to account for improved resource
 tterm <- 1 - (1/(3*lambda)) * (varphi - (lambda * (L/KU)))^3      #              allocation
 newtterm <- 1 - (1/(3*newlambda)) * (newvarphi - (newlambda * (newL/KU)))^3  # tterm modified
#                                                  # to account for improved resource allocation
# When K is normalized at unity, the full-employment level of output will
#  equal
#
 Yf <- mterm * tterm
 newYf <- newmterm * newtterm    # full-employment output under improved resource allocation
#
 acterm <- 1 + (2 * alpha) * (g + (KU - 1)* Yf)
 newacterm <- 1 + (2 * alpha) * (g + (KU - 1)* newYf)   # impose modifications on  acterm
 dmterm <- ((varphi - (lambda * (L/KU)))^2) - inf
 newdmterm <- ((newvarphi - (newlambda * (newL/KU)))^2) - inf  # impose modifications
#
# The full-employment level of r should also equal ssgterm
#
 ssgterm <- ((1 + varpi)*(1 + g) / (1 - tau)) - 1
#
 cat(r);cat("\n")             # Print the original values together with the
 cat(newr);cat("\n")          #   ones that result after the improvement 
 cat(ssgterm);cat("\n")       #   of resource allocation
 cat(Yf);cat("\n")
 cat(newYf);cat("\n")
 cat(varphi);cat("\n")
 cat(newvarphi);cat("\n")
 cat(lambda);cat("\n")
 cat(newlambda);cat("\n")
#
# CALCULATE POINTS ON THE AA AND GG CURVES FOR KU = .96, .97, .98, .99,
#   1.00, 1.01, 1.02, 1.03, 1.04, 1.05, 1.06  -- which can be viewed as the
#   ratio of actual output to full-employment output  
#
 yvec <- c(0.96,0.97,0.98,0.99,1.00,1.01,1.02,1.03,1.04,1.05,1.06)  # set the levels
#    of KU for which interest rate levels on the GG and AA curves will be calculated.
#
#  Start with the GG curve --- equation (7) in the document 
#
 KU <- 0.96
#
 acterm <- 1 + (2 * alpha * g) + (2 * sralpha * (KU - 1)* Yf)
 tterm <- 1 - (1/(3*lambda)) * (varphi - (lambda * (L/KU)))^3
 rg <- (mterm / acterm) * tterm   # level of r on the GG curve
 rggvec <- c(rg)   # create the first element on a vector of values
#
 KU <- 0.97
#
 acterm <- 1 + (2 * alpha * g) + (2 * sralpha * (KU - 1)* Yf)
 tterm <- 1 - (1/(3*lambda)) * (varphi - (lambda * (L/KU)))^3
 rg <- (mterm / acterm) * tterm
 rggvec <- c(rggvec, rg)   # add element to the vector of values
#
# Calculate the remaining values using a for loop
#
 for (i in 1:9){
 KU <- KU + .01
 acterm <- 1 + (2 * alpha * g) + (2 * sralpha * (KU - 1)* Yf)
 tterm <- 1 - (1/(3*lambda)) * (varphi - (lambda * (L/KU)))^3
 rg <- (mterm / acterm) * tterm
 rggvec <- c(rggvec, rg)  # add elements one-by-one to the vector of values
 }
#
# rggvec is a list of values of r on the GG curve for the above-noted
#  values of KU  
#
# Now perform the same calculations for the AA curve  --- equation (8) in the document
#
 KU <- .96
 dmterm <- (varphi - (lambda * (L/KU)))^2
 ra <- mterm * dmterm - inf     # inf is inflation rate (fraction, not percent)
 raavec <- c(ra)
 for (i in 1:10){
 KU <- KU + .01
 dmterm <- (varphi - (lambda * (L/KU)))^2
 ra <- mterm * dmterm - inf     
 raavec <- c(raavec, ra)
 }
#
# raavec is a list of values of r on the AA curve for the above-noted
#  values of KU
#
# Impose a Monetary Shock taking the form of a 1.5% increase in L
#
L <- 1.015 * L
KU <- .96
 dmterm <- (varphi - (lambda * (L/KU)))^2
 sra <- mterm * dmterm - inf   
 sraavec <- c(sra)
 for (i in 1:10){
 KU <- KU + .01
 dmterm <- (varphi - (lambda * (L/KU)))^2
 sra <- mterm * dmterm - inf  
 sraavec <- c(sraavec, sra)
 }
# Multiply raavec sraavec and rggvec by 100 to put the interest rates in 
#  percentage terms
#
raavec <- 100 * raavec
sraavec <- 100 * sraavec
rggvec <- 100 * rggvec
#
yvec
raavec
sraavec
rggvec
#
postscript("GGAA1r.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE)
plot(yvec,raavec,type="l",
xlim = c(.9575,1.0625),
ylim = c(0.5,11),
xlab="Ratio of Actual to Full-Employment Income",
ylab="Interest Rate -- Percent",main="AA and GG Curves: Monetary Shock")
lines(yvec[3:11],sraavec[3:11],lty=2)
lines(yvec,rggvec,lty=1)
#legend(1.001,6.75,c("AA","GG"),lty=c(1,2))
abline(v=1.0)
#abline(h=3.963631)
text(0.9575,5.9,"G")
text(1.0627,2.65,"G")
text(0.9575,0.59,"A")
text(1.0623,10.75,"A")
text(0.9775,0.97,"A'")
text(1.0627,8.78,"A'")
text(1.011,4.1,"b")
text(0.9975,4.5,"a")
dev.off()
#
# Impose Real Shocks
#
# The real interest rate associated with a level of income 4%
#  above the old full-employment income was the 9th element in
#  rggvec.
#
 rgg9 <- rggvec[9]
#
# Raise all elements of rggvec by the proportion newr/rgg9
#
 srggvec <- (100*newr/rgg9) * rggvec   # multiply by 100 because newr is a fraction, not a
#                                                                        percentage.
# Make second figure to show the effects of real shocks
#
postscript("GGAA2r.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE)
plot(yvec,raavec,type="l",
xlim = c(.9575,1.0625),
ylim = c(0.5,11),
xlab="Ratio of Income to Initial Full-Employment Income",
ylab="Interest Rate -- Percent",main="AA and GG Curves: Real Shocks")
lines(yvec,rggvec,lty=1)
lines(yvec,srggvec,lty=2)
abline(v=1.0)
abline(v=(newYf/Yf),lty=2)
abline(h=(100*r),lty=3)
text(0.9575,5.9,"G")
text(1.0627,2.65,"G")
text(0.9575,7.9,"G'")
text(1.0627,3.57,"G'")
text(0.9575,0.59,"A")
text(1.0623,10.75,"A")
text(0.9975,4.5,"a")
text(1.042,4.37,"c")
text(1.00195,5.67,"d")
text(1.0095,5.45,"b")
dev.off()
#
# Make third figure to show the effects of an increase in the distortionary
#    tax on savings using information obtained with GGAAssg.R
#
# make a new vector that incorporates the upward effect of an increase in
#  tau from .01 to .015 on r at Y/Yf of 1.00
#
ssrggvec <- (0.04232256 / 0.03961631) * rggvec     # numbers are from  GGAAssg.xls
#
postscript("GGAA3r.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE)
plot(yvec,raavec,type="l",
xlim = c(.9575,1.0625),
ylim = c(0.5,11),
xlab="Ratio of Income to Initial Full-Employment Income",
ylab="Interest Rate -- Percent",main="AA and GG Curves: Tax on Savings")
lines(yvec,rggvec,lty=1)
lines(yvec,ssrggvec,lty=2)
abline(v=1.0)
abline(v=(0.06192969/0.06193458),lty=2)
text(0.9575,5.9,"G")
text(1.0627,2.65,"G")
text(0.9575,0.59,"A")
text(1.0623,10.75,"A")
abline(h=(100*r),lty=3)
dev.off()
# 
#  Extend the results to small open economy by imposing a rest-of-world
#     established real interest rate -- choose the initial full-employment rate
#
wrldr <- rep(r,11)      # generate horizontal interest rate line
wrldr
#
# Plot the case of monetary policy under a fixed exchange rate
#
postscript("GGAA4r.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE)
plot(yvec,raavec,type="l",
xlim = c(.9575,1.0625),
ylim = c(0.5,11),
xlab="Ratio of Actual to Full-Employment Income",
ylab="Interest Rate -- Percent",main="Open Economy: Monetary Shock, Fixed Exchange Rate")
lines(yvec[3:11],sraavec[3:11],lty=2)
lines(yvec,rggvec,lty=1)
lines(yvec,100*wrldr,lty=1)
abline(v=1.0)
#abline(h=3.963631)
text(0.9575,5.9,"G")
text(1.0627,2.65,"G")
text(0.9575,0.59,"A")
text(1.0623,10.75,"A")
text(0.9775,0.97,"A'")
text(1.0627,8.78,"A'")
#text(1.011,4.1,"b")
text(0.9575,4,"r")
text(1.0627,4,"Z")
text(0.9975,4.5,"a")
text(1.018,5,"---->")
text(1.013,4.5,"<----")
dev.off()
#
# Plot the case of monetary policy under a flexible exchange rate
#
#   Create a GG curve that passes through the new equilibrium point
#
rggvecmfl <- 1.12*rggvec
#
postscript("GGAA5r.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE)
plot(yvec,raavec,type="l",
xlim = c(.9575,1.0625),
ylim = c(0.5,11),
xlab="Ratio of Actual to Full-Employment Income",
ylab="Interest Rate -- Percent",main="Small Open Economy: Monetary Shock, Flexible Exchange Rate")
lines(yvec[3:11],sraavec[3:11],lty=2)
lines(yvec,rggvec,lty=1)
lines(yvec,100*wrldr,lty=1)
lines(yvec,rggvecmfl,lty=2)
abline(v=1.0)
#abline(h=3.963631)
text(0.9575,5.9,"G")
text(1.0627,2.65,"G")
text(0.9575,0.59,"A")
text(1.0623,10.75,"A")
text(0.9775,0.97,"A'")
text(1.0627,8.78,"A'")
text(1.015,4.49,"b")
text(0.9575,4,"r")
text(1.0627,4,"Z")
text(1.0020,3.5,"a")
dev.off()
#
# Plot the case of a positive real shock under a fixed exchange rate
#
rggvecrfi <- 1.135*rggvec
#
postscript("GGAA6r.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE)
plot(yvec,raavec,type="l",
xlim = c(.9575,1.0625),
ylim = c(0.5,11),
xlab="Ratio of Actual to Full-Employment Income",
ylab="Interest Rate -- Percent",main="Small Open Economy: Real Shock, Fixed Exchange Rate")
lines(yvec,rggvecrfi,lty=2)
lines(yvec[3:11],sraavec[3:11],lty=2)
lines(yvec,rggvec,lty=1)
lines(yvec,100*wrldr,lty=1)
abline(v=1.0)
text(0.9575,5.9,"G")
text(0.9575,6.7,"G'")
text(1.0627,2.50,"G")
text(1.0627,3.10,"G'")
text(0.9575,0.59,"A")
text(1.0623,10.75,"A")
text(1.015,4.5,"b")
text(0.9575,4,"r")
text(1.0627,4,"Z")
text(1.0020,3.5,"a")
dev.off()
#
# Plot the case of a positive real shock under a flexible exchange rate
#
rggvecrfl <- 1.20*rggvec    #make the shock slightly larger than in the fixed exchange rate case
#
postscript("GGAA7r.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE)
plot(yvec,raavec,type="l",
xlim = c(.9575,1.0625),
ylim = c(0.5,11),
xlab="Ratio of Actual to Full-Employment Income",
ylab="Interest Rate -- Percent",main="Small Open Economy: Real Shock, Flexible Exchange Rate")
lines(yvec,rggvecrfl,lty=2)
lines(yvec,rggvec,lty=1)
lines(yvec,100*wrldr,lty=1)
abline(v=1.0)
text(0.9575,5.9,"G")
text(1.0627,2.65,"G")
text(0.9575,0.59,"A")
text(1.0623,10.75,"A")
text(0.9575,4,"r")
text(1.0627,4,"Z")
text(0.9975,4.5,"a")
text(0.975,5.5,"<----")
text(0.985,5,"---->")
dev.off()
#
#  Put results in matrix form and print them to screen
#
GGAAmatr <- cbind(yvec, raavec, sraavec, rggvec, srggvec, ssrggvec, rggvecmfl, rggvecrfi, rggvecrfl)
#
GGAAmatr
#