# R SCRIPT FILE TO CALULATE THE DEMAND FUNCTION FOR LIQIDITY
#
# Define and set the magnitudes of the parameters
#
mhat <- .14          # optimal output flow as fraction of capital stock
delta <- .05         # depreciation rate
gamma <- .2          # resource missallocation parameter
phi <- 8.94          # first demand for money parameter
lambda <- 298.14     # second demand for money parameter
#
# Set the range of levels of the liquidity/capital ratio as
#      0 through 3000
#
LKR <- rep(0,3000)    # start with 3000 zeros
for (j in 2:3001){    # set values to represent alternative 
LKR[j]=LKR[j-1]+1     #   levels of the liquidity/capital ratio 
}                     #   ranging from 0 through 3000
#
#  Adjust the scale of the liquidity/capital ratio and then
#   calculate the optimum level of the income/capital ratio. 
#   Then construct an additional income/capital ratio that is
#   20 percent higher
#
LKR <- LKR/100000                  # set the scale of the liquidity capital ratio
YKR <- (mhat*(1-gamma)-delta)      # optimum liquidity ratio of income to capital
YKR2 <- 1.2*YKR                    # increase above income/capital ratio by 20 percent
#
#  Calculate the marginal return to liquidity for the two income/capital ratios
#
MRL <- YKR*(phi - lambda*LKR)^2    # marginal return to liquidity
MRL2 <- YKR2*(phi - lambda*LKR)^2  # marginal return to liquidity when income/capital
#                                     ratio is increased by 20 percent
LYR <- LKR/YKR                     # calculate the liquity/income ratio  
#
plot(100*LKR,100*MRL,type="l",     # plot the two variables as percentages
xlab="Liquidity as Percentage of the Capital Stock",
ylab="Marginal Return -- Percent Per Annum",
main="Marginal Return to Liquidity")
#
#
LYRS <- LYR[2500:3000]             # select only the last 500 elements of the
MRLS <- MRL[2500:3000]             #   series
MRL2S <- MRL2[2500:3000]
# 
plot(100*LYRS,100*MRLS,lty=1,type="l", 
xlab="Real Stock of Liquidity as Percentage of Income",
ylab="Nominal Interest Rate",
main="The Demand Function for Liquidity")
lines(100*LYRS,100*MRL2S,lty=2,type="l")
legend(44.8,14,c("Real Income = 100","Real Income = 120"),lty=c(1,2))
#
# Save above plots in jpg and endapsulated postscript files
#
jpeg(filename = "mrliq.jpg", width = 800, height = 500, 
#units = "px",
pointsize = 12, quality = 150, bg = "white", res = NA, restoreConsol = TRUE)
plot(100*LKR,100*MRL,type="l",
xlab="Liquidity as Percentage of the Capital Stock",
ylab="Marginal Return -- Percent Per Annum",
main="The Marginal Return to Liquidity")
dev.off()
#
postscript("mrliq.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE) 
plot(100*LKR,100*MRL,type="l",
xlab="Liquidity as Percentage of the Capital Stock",
ylab="Marginal Return -- Percent Per Annum",
main="The Marginal Return to Liquidity")
dev.off()
#
jpeg(filename = "demliq.jpg", width = 800, height = 500, 
#units = "px",
pointsize = 12, quality = 150, bg = "white", res = NA, restoreConsol = TRUE)
plot(100*LYRS,100*MRLS,type="l",
xlab="Real Stock of Liquidity",
ylab="Nominal Interest Rate",
main="The Demand Function for Liquidity")
lines(100*LYRS,100*MRL2S,lty=2,type="l")
legend(44.8,14,c("Income = 100","Income = 120"),lty=c(1,2))
dev.off()
#
postscript("demliq.eps",paper="letter",width=6.5,height=4.5,horizontal=FALSE) 
plot(100*LYRS,100*MRLS,type="l",
xlab="Real Stock of Liquidity",
ylab="Nominal Interest Rate",
main="The Demand Function for Liquidity")
lines(100*LYRS,100*MRL2S,lty=2,type="l")
legend(44.8,14,c("Income = 100","Income = 120"),lty=c(1,2))
dev.off()
#