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andrew_base.R
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#library(EIAdata)
library(nleqslv)
library(curl)
library(janitor)
library(viridis)
library(scales)
library(openxlsx)
library(reshape2)
library(zoo)
library(RColorBrewer)
library(scales)
library(pdfetch)
library(tidyverse)
library(XML)
library(lubridate)
library(httr)
library(jsonlite)
library(readxl)
library(rvest)
library(forcats)
library(ggrepel)
library(ggpubr)
library(gridExtra)
library(timeDate)
library(cansim)
library(ggthemes)
working_directory<-getwd()
#Mac
if(R.version$platform == "x86_64-apple-darwin15.6.0")
setwd("/Users/aleach/Google Drive/")
#PC
if(R.version$platform == "x86_64-w64-mingw32")
setwd("C:/Users/aleach/Google Drive/")
#print(getwd())
#setwd("G:/My Drive")
source("tableau.R")
set_png<-function(file_sent,width=1400,height=750,res=130){
#MAC
if(R.version$platform == "x86_64-apple-darwin15.6.0")
png(file=file_sent, width = width, height = height,res=res)
#PC
if(R.version$platform == "x86_64-w64-mingw32")
png(file=file_sent, width = width, height = height,res=res,type='cairo')
}
ajl_hourly<-function(){
theme_minimal()+theme(
legend.position = "bottom",
legend.margin=margin(c(0,0,0,0),unit="cm"),
legend.text = element_text(colour="black", size = 18, face = "bold"),
plot.caption = element_text(size = 14, face = "italic"),
plot.title = element_text(face = "bold"),
plot.subtitle = element_text(size = 16, face = "italic"),
panel.grid.minor = element_blank(),
text = element_text(size = 14,face = "bold"),
axis.text = element_text(size = 14,face = "bold", colour="black")
)
}
blake_theme<-function(){
theme_hc(20)+
theme(plot.subtitle = element_text(color="grey10",size=rel(.7)),
plot.title = element_text(face="bold",size=rel(.8)),
plot.caption = element_text(color="grey50",size=rel(.5),hjust=0),
legend.title = element_text(color="grey10",size=rel(.5)),
legend.text = element_text(color="grey10",size=rel(.5)),
axis.title = element_text(size=rel(.8)),
axis.ticks = element_blank(),
panel.spacing = unit(2,"lines"),
#legend.position = "none",
plot.margin = margin(t = .5, r = 1, b = .25, l = 1,unit= "cm"),
axis.text.x = element_text(margin = margin(t = 10, r = 0, b = 0, l = 0))
)
}
ajl_line<-function(caption_align=1){
theme_linedraw()+theme(
plot.margin = margin(.5, .5, .5, .5, "cm"),
legend.position = "bottom",
legend.margin=margin(c(0,0,0,0),unit="cm"),
legend.text = element_text(colour="black", size = 14, face = "bold"),
plot.caption = element_text(size = 14, face = "italic",hjust=caption_align),
plot.title = element_text(face = "bold"),
plot.subtitle = element_text(size = 16, face = "italic"),
panel.grid.minor = element_blank(),
text = element_text(size = 14,face = "bold"),
axis.text = element_text(size = 14,face = "bold", colour="black",margin = margin(t = 10, b = 5)),
)
}
make_breaks <- function(strt, hour, interval="day", length.out=31) {
strt <- as.POSIXlt(strt - 60*60*24) # start back one day
strt <- ISOdatetime(strt$year+1900L, strt$mon+1L, strt$mday, hour=hour, min=0, sec=0, tz="UTC")
seq.POSIXt(strt, strt+(1+length.out)*60*60*24, by=interval)
}
slide_theme<-function(){
return( theme(panel.border = element_blank(),
panel.grid = element_blank(),
panel.grid.major.y = element_line(color = "gray",linetype="dotted"),
axis.line.x = element_line(color = "gray"),
axis.line.y = element_line(color = "gray"),
axis.text = element_text(size = 16),
axis.text.x = element_text(margin = margin(t = 10)),
axis.title = element_text(size = 16),
#axis.label.x = element_text(size=20,vjust=+5),
plot.subtitle = element_text(size = 12,hjust=0.5),
plot.caption = element_text(face="italic",size = 12,hjust=0),
legend.key.width=unit(2,"line"),
legend.position = "bottom",
#legend.direction = "horizontal",
#legend.box = "horizontal",
legend.title = element_text(size = 16),
legend.text = element_text(size = 16),
plot.title = element_text(hjust=0.5,size = 20),
plot.margin=unit(c(1,1,1.5,1.2),"cm")
)
)
}
small_theme<-function(){
return( theme(panel.border = element_blank(),
panel.grid = element_blank(),
panel.grid.major.y = element_line(color = "gray",linetype="dotted"),
axis.line.x = element_line(color = "gray"),
axis.line.y = element_line(color = "gray"),
axis.text = element_text(size = 12),
axis.text.x = element_text(margin = margin(t = 10)),
axis.title = element_text(size = 12),
#axis.label.x = element_text(size=20,vjust=+5),
plot.subtitle = element_text(size = 12,hjust=0.5),
plot.caption = element_text(face="italic",size = 8,hjust=0),
legend.key.width=unit(2,"line"),
legend.position = "bottom",
#legend.direction = "horizontal",
#legend.box = "horizontal",
legend.title = element_text(size = 12),
legend.text = element_text(size = 12),
plot.title = element_text(hjust=0.5,size = 14),
plot.margin=unit(c(1,1,1.5,1.2),"cm")
)
)
}
weekly_graphs<-function(caption_align=1){
theme_minimal()+theme(
plot.margin = margin(.25, .75, .25, .75, "cm"),
legend.position = "bottom",
legend.margin=margin(c(0,0,0,0),unit="cm"),
legend.text = element_text(colour="black", size = 14, face = "bold"),
plot.caption = element_text(size = 10, face = "italic",hjust=caption_align),
plot.title = element_text(face = "bold"),
plot.subtitle = element_text(size = 12, face = "italic"),
panel.grid.minor = element_blank(),
text = element_text(size = 14,face = "bold"),
axis.title.x = element_text(size = 14,face = "bold", colour="black",margin = margin(t = 15, b = 0)),
axis.text = element_text(size = 14,face = "bold", colour="black",margin = margin(t = 10, b = 10)),
)
}
weekly_small<-function(caption_align=1){
theme_minimal()+theme(
plot.margin = margin(.25, .75, .25, .75, "cm"),
legend.position = "bottom",
legend.margin=margin(c(0,0,0,0),unit="cm"),
legend.text = element_text(colour="black", size = 9),
plot.caption = element_text(size = 11, face = "italic",hjust=caption_align),
plot.title = element_text(size = 16,face = "bold"),
plot.subtitle = element_text(size = 14, face = "italic"),
panel.grid.minor = element_blank(),
text = element_text(size = 11,face = "bold"),
axis.title.x = element_text(size = 11,face = "bold", colour="black",margin = margin(t = 15, b = 0)),
axis.text = element_text(size = 11,face = "bold", colour="black",margin = margin(t = 10, b = 10)),
)
}
tombe_theme<-function(caption_align=1){
theme_minimal()+theme(
axis.title.y = element_text(size=12),
axis.title.x = element_text(size=12),
axis.text = element_text(size=12),
legend.position = "bottom",
legend.text=element_text(size=12),
legend.margin=margin(c(0,0,-0.25,0),unit="cm"),
plot.caption = element_text(size = 8, color = "gray40",hjust=0),
plot.title = element_text(face = "bold"),
plot.subtitle = element_text(size = 10, color = "gray40"),
panel.grid.minor = element_blank(),
panel.grid.major.x = element_blank()
)
}
#EIA stuff
data_fetch<-function(key, cat=2227122){
key <- unlist(strsplit(key, ";"))
ifelse(cat==999999999,
url <- paste("http://api.eia.gov/category?api_key=",
key, "&out=xml", sep="" ),
url <- paste("http://api.eia.gov/category?api_key=",
key, "&category_id=", cat, "&out=xml", sep="" )
)
doc <- xmlParse(file=url, isURL=TRUE)
Parent_Category <- tryCatch(xmlToDataFrame(,stringsAsFactors = F,nodes =
XML::getNodeSet(doc, "//category/parent_category_id")),
warning=function(w) FALSE, error=function(w) FALSE)
Sub_Categories <- xmlToDataFrame(,stringsAsFactors = F,nodes =
XML::getNodeSet(doc, "//childcategories/row"))
Series_IDs <- xmlToDataFrame(nodes =
XML::getNodeSet(doc, "///childseries/row"),stringsAsFactors = F)
Categories <- list(Parent_Category, Sub_Categories, Series_IDs)
names(Categories) <- c("Parent_Category", "Sub_Categories", "Series_IDs")
return(Categories)
}
# store_packages.R
#
# stores a list of your currently installed packages
#tmp = installed.packages()
#installedpackages = as.vector(tmp[is.na(tmp[,"Priority"]), 1])
#save(installedpackages, file="installed_packages.rda")
# restore_packages.R
#
# installs each package from the stored list of packages
#load("installed_packages.rda")
#
#for (count in 1:length(installedpackages)) install.packages(installedpackages[count])
#remotes::install_github("mountainmath/cansim")
#havingIP <- function() {
# if (.Platform$OS.type == "windows") {
# ipmessage <- system("ipconfig", intern = TRUE)
# } else {
# ipmessage <- system("ifconfig", intern = TRUE)
# }
# validIP <- "((25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)[.]){3}(25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)"
# any(grep(validIP, ipmessage))
#}
#havingIP()
#revert to previous working directory
setwd(working_directory)
print(getwd())
wordwrap<-function(x,len) paste(strwrap(x,width=len),collapse="\n")
#convert to two decimal places for currency labels
scale_dec2 <- function(x) sprintf("%.2f", x)
assign_peaks<-function(data_orig,time_var=time){
#default is that we're receiving a data_frame with time as the time variable
#create temp_time with whatever the time variable might be, then use that to create stats and peaks
#modify data_sent so you have a data-frame with only the time varible
#data_mod<-data_orig %>% mutate_(temp_time=`time_var`) %>% select(temp_time)
temp_time<- enquo(time_var)
data_mod<-data_orig%>% select(!!temp_time)
#first, figure out the holidays
#Holidays:
#xNew Year's Day January 1
#xAlberta Family Day Third Monday in February
#xGood Friday Friday before Easter
#Victoria Day Monday before May 25
#xCanada Day July 1, except when it falls on a Sunday, then it is July 2
#xLabour Day First Monday in September
#xThanksgiving Day Second Monday in October
#xRemembrance Day November 11
#xChristmas Day December 25
holiday_list<-c("Christmas","NYD","CDA_Day","Rem_Day","Labour_Day","Good_Friday","Family_Day",
"Thanksgiving", "Victoria_Day")
data_mod<-data_mod%>%mutate(
Christmas=ifelse(month(!!temp_time)==12 & day(!!temp_time)==25,T,F),
NYD=ifelse(month(!!temp_time)==1 & day(!!temp_time)==1,T,F),
CDA_Day=ifelse(month(!!temp_time)==7 & day(!!temp_time)==1 & wday(!!temp_time,label = T)!="Sun" ,T,F), #Canada Day Holiday if it's not a Sunday
CDA_Day=ifelse(month(!!temp_time)==7 & day(!!temp_time)==2 & wday(!!temp_time,label = T)=="Mon" ,T,F), #Canada Day Stat if the 2nd is a monday
Rem_Day=ifelse(month(!!temp_time)==11 & day(!!temp_time)==11,T,F),
Labour_Day=ifelse(month(!!temp_time)==9 & day(!!temp_time)<=7 & wday(!!temp_time,label = T)=="Mon",T,F), #first Monday in September
Good_Friday=ifelse(date(!!temp_time)==as.Date(Easter(year(!!temp_time)))-days(2),T,F),
#Family day - third monday in february so earliest it can be is day 15, latest is day 21
Family_Day=ifelse(month(!!temp_time)==2 & day(!!temp_time)<=21 & day(!!temp_time)>=15 & wday(!!temp_time,label = T)=="Mon",T,F), #third Monday in Feb
#Thanksgiving day - second monday in Oct so earliest it can be is day 8, latest is day 14
Thanksgiving=ifelse(month(!!temp_time)==10 & day(!!temp_time)<=14 & day(!!temp_time)>=8 & wday(!!temp_time,label = T)=="Mon",T,F), #second Monday in Oct
#Victoria day - monday before May 25, so earliest it can be is day 18, latest is day 24
Victoria_Day=ifelse(month(!!temp_time)==5 & day(!!temp_time)<=24 & day(!!temp_time)>=18 & wday(!!temp_time,label = T)=="Mon",T,F) #Monday before May 25
) %>% mutate(
stat = select(., holiday_list) %>% rowSums()>0
)
#On-Peak: hour ending HE8 to HE23 Monday through Saturday, excluding Sundays and NERC holidays
#Off-Peak: HE1 to HE7 and HE24 Monday through Saturday, and all hours on Sundays and NERC holidays
#Extended Peak: HE8 to HE23 every day in the contract period
#Extended Off-Peak: HE1 to HE7 and HE24 every day in the contract period
#Super Peak: HE17 to HE22 each day in the contract period
#for AS, AESO does AM super peak HE 6, 7, 8 and a winter PM Super Peak (HE 17-34, in Nov, Dec, Jan)
data_mod<-data_mod%>%mutate(
on_peak=ifelse(wday(!!temp_time,label = T)!="Sun" & stat==F & hour(!!temp_time)>=8 & hour(!!temp_time)<=23,T,F), #Peak hours, not stat or Sunday
off_peak=ifelse(wday(!!temp_time,label = T)=="Sun" | stat==T | hour(!!temp_time)>=24 | hour(!!temp_time)<=7,T,F), #Off-Peak hours, stat or Sunday
ext_peak=ifelse(hour(!!temp_time)>=8 & hour(!!temp_time)<=23,T,F), #Ext Peak hours
ext_off_peak=ifelse(hour(!!temp_time)<8 & hour(!!temp_time)>23,T,F), #Ext Off Peak hours
super_peak=ifelse(hour(!!temp_time)>=17 & hour(!!temp_time)<=22,T,F), #Super Peak hours
)
#return indicators for stats and peaks - same # of rows as data sent
data_mod<-data_mod %>% select(stat,on_peak,off_peak,ext_peak,ext_off_peak,super_peak)
bind_cols(data_orig,data_mod)
}
assign_date_time_days<-function(data_sent,time_var=time){
quo_time<- enquo(time_var)
data_sent %>%
mutate(year=year(!!quo_time),
month=month(!!quo_time), #month dummies
month_fac=factor(month.abb[month],levels = month.abb),
day=day(!!quo_time),
wday=wday(!!quo_time,label=T),
hour=hour(!!quo_time),
temp_time=NULL
)
}
#create time from date and he
#assign_time<-function(data_sent,date_var="date",he_var="he"){
# data_sent %>% mutate_(temp_date=`date_var`,temp_he=`he_var`) %>%
# mutate(time=ymd_h(paste(year(temp_date),"-",month(temp_date),"-",month(temp_date)," ",temp_he,sep="")),
# temp_date=NULL,
# temp_he=NULL
# )
#}
assign_time <- function(data, date_var=date, he_var=he){
quo_date <- enquo(date_var)
quo_he <- enquo(he_var)
data %>%
mutate(time = ymd_h(paste(year(!!quo_date), "-",
month(!!quo_date), "-",
day(!!quo_date), "-",
!!quo_he, sep = "")))
}
#u of a palette
colors_ua10 <- function()
{
#return(c("#007C41", "#FFDB05", "#7D9AAA", "#CA7700", "#165788", "#A8B400",
# "#E0D760", "#404545", "#8D3C1E", "#004250"))
c("#007C41", "#FFDB05", "#7D9AAA","#165788","#404545","#8D3C1E","#3CB6CE")
}
#You really can only have one of c("#FFDB05", "#A8B400","#E0D760")
Mode <- function(x) {
ux <- unique(x)
ux[which.max(tabulate(match(x, ux)))]
}
theme_slides <- theme_classic() +
theme(
text = element_text(family = "Fira Sans", size = 24)
)
supply_1=function(x){x}
mpc=function(x){x-2}
demand_1=function(x){10-x}
mr=function(x){10-2*x}
ce<-
ggplot(data.frame(x=c(0,10)), aes(x=x))+
stat_function(fun=demand_1, geom="line", size=2, color = "blue")+
geom_label(aes(x=10,y=demand_1(10),hjust=0.5), nudge_y = +rel(1.25), color = "blue", label=str_wrap("Demand = Marginal Benefit",10), size = rel(3.5))+
stat_function(fun=supply_1, geom="line", size=2, color = "firebrick")+
geom_label(aes(x=10,y=supply_1(10),hjust=.5), nudge_y = -rel(1.25), color = "firebrick", label=str_wrap("Supply = Marginal Cost",10), size = rel(3.5))+
geom_label(aes(x=5,y=0,hjust=.5), nudge_y = -rel(.75), color = "black", label=str_wrap("Competitive Market Quantity",10), size = rel(3.5))+
geom_label(aes(x=0,y=5,hjust=.5), nudge_x = -rel(.75), color = "black", label=str_wrap("Competitive Market Price",10), size = rel(3.5))+
geom_segment(x=0, xend=5, y=5, yend=5, size=1, linetype="dotted")+
geom_segment(x=5, xend=5, y=0, yend=5, size=1, linetype="dotted")+
scale_x_continuous(breaks=seq(0,10,1))+
scale_y_continuous(breaks=seq(0,10,1),
labels = function(x){paste("$", x, sep="")},
limits = c(-1,10))+
expand_limits(x = c(0,10.5),y=c(0,10))+
labs(x = "Quantity (q)",
y = "Price (p)")+
blake_theme()+
theme(plot.margin = margin(t = .1, r = .1, b = .1, l = .1,unit= "cm"))+
NULL
ce
ggsave("graph_ce.png",width = 10,height = 10)
mp<-
ggplot(data.frame(x=c(0,10)), aes(x=x))+
stat_function(fun=demand_1, geom="line", size=2, color = "blue")+
geom_label(aes(x=10,y=demand_1(10),hjust=0.5), nudge_x = rel(.5), color = "blue", label=str_wrap("Marginal Social Benefit",10), size = rel(3.5))+
stat_function(fun=mr, linetype="dashed", size=2, color = "blue")+
geom_label(aes(x=1.25,y=mr(1.25),hjust=1),nudge_x = +rel(.5), color = "blue", label=str_wrap("Marginal Revenue",10), size = rel(3.5))+
geom_segment(x=0, xend=5, y=5, yend=5, size=1, linetype="dotted")+
geom_segment(x=5, xend=5, y=0, yend=5, size=1, linetype="dotted")+
geom_label(aes(x=5,y=0,hjust=.5), nudge_x = rel(.5), color = "black", label=str_wrap("Competitive Market Quantity",10), size = rel(3.5))+
geom_label(aes(x=0,y=5,hjust=.5), nudge_x = -rel(.2), color = "black", label=str_wrap("Competitive Market Price",10), size = rel(3.5))+
stat_function(fun=supply_1, geom="line", size=2, color = "firebrick")+
geom_label(aes(x=10,y=supply_1(10),hjust=.5), nudge_x = rel(.5), color = "firebrick", label=str_wrap("Marginal Social Cost",10), size = rel(3.5))+
geom_segment(x=10/3, xend=10/3, y=0, yend=demand_1(10/3), size=1, linetype="dotted",color="black")+
geom_segment(x=0, xend=10/3, y=demand_1(10/3), yend=demand_1(10/3), size=1, linetype="dotted",color="black")+
geom_segment(x=0, xend=10/3, y=supply_1(10/3), yend=supply_1(10/3), size=1, linetype="dotted",color="black")+
geom_label(aes(x=10/3,y=0,hjust=.5), nudge_x = -rel(.5), color = "black", label=str_wrap("Monopoly Quantity",10), size = rel(3.5))+
geom_label(aes(x=0,y=supply_1(10/3),hjust=.5), nudge_x = -rel(.2),color = "black", label=str_wrap("Monopoly Marginal Cost",10), size = rel(3.5))+
geom_label(aes(x=0,y=demand_1(10/3),hjust=.5), nudge_x = -rel(.2),color = "black", label=str_wrap("Monopoly Price",10), size = rel(3.5))+
scale_x_continuous(breaks=seq(0,10,1))+
scale_y_continuous(breaks=seq(0,10,1),
labels = function(x){paste("$", x, sep="")},
limits = c(0,10))+
expand_limits(x = c(0,10.5),y=c(0,10))+
labs(x = "Quantity (q)",
y = "Price (p)")+
blake_theme()+
theme(plot.margin = margin(t = .1, r = .1, b = .1, l = .1,unit= "cm"))+
NULL
mp
ggsave("graph_mp.png",width = 10,height = 10)
dwl_neg<-tribble(
~x, ~y,
10/3,10-10/3,
5, 5,
10/3, 10-20/3
)
mp2<-
ggplot()+
geom_polygon(data = dwl_neg,
aes(x = x,
y = y),
fill = "black",
alpha = 0.3)+
geom_text_repel(aes(x=4,y=5),label=str_wrap("Welfare loss from monopoly",10),
nudge_y = 2.1,
nudge_x = 1,
direction = "x",
vjust = 0,
segment.size = 0.2
)+
stat_function(fun=demand_1, geom="line", size=2, color = "blue")+
geom_label(aes(x=10,y=demand_1(10),hjust=0.5), nudge_x = rel(.5), color = "blue", label=str_wrap("Marginal Social Benefit",10), size = rel(3.5))+
stat_function(fun=mr, linetype="dashed", size=2, color = "blue")+
geom_label(aes(x=1.25,y=mr(1.25),hjust=1),nudge_x = +rel(.5), color = "blue", label=str_wrap("Marginal Revenue",10), size = rel(3.5))+
geom_segment(aes(x=0, xend=5, y=5, yend=5), size=1, linetype="dotted")+
geom_segment(aes(x=5, xend=5, y=0, yend=5), size=1, linetype="dotted")+
geom_label(aes(x=5,y=0,hjust=.5), nudge_x = rel(.5), color = "blue", label=str_wrap("Competitive Market Quantity",10), size = rel(3.5))+
geom_label(aes(x=0,y=5,hjust=.5), nudge_x = -rel(.2), color = "blue", label=str_wrap("Competitive Market Price",10), size = rel(3.5))+
stat_function(fun=supply_1, geom="line", size=2, color = "firebrick")+
geom_label(aes(x=10,y=supply_1(10),hjust=.5), nudge_x = rel(.5), color = "firebrick", label=str_wrap("Marginal Social Cost",10), size = rel(3.5))+
geom_segment(aes(x=10/3, xend=10/3, y=0, yend=demand_1(10/3)), size=1, linetype="dotted",color="black")+
geom_segment(aes(x=0, xend=10/3, y=demand_1(10/3), yend=demand_1(10/3)), size=1, linetype="dotted",color="black")+
geom_segment(aes(x=0, xend=10/3, y=supply_1(10/3), yend=supply_1(10/3)), size=1, linetype="dotted",color="black")+
geom_label(aes(x=10/3,y=0,hjust=.5), nudge_x = -rel(.5), color = "black", label=str_wrap("Monopoly Quantity",10), size = rel(3.5))+
geom_label(aes(x=0,y=supply_1(10/3),hjust=.5), nudge_x = -rel(.2),color = "black", label=str_wrap("Monopoly Marginal Cost",10), size = rel(3.5))+
geom_label(aes(x=0,y=demand_1(10/3),hjust=.5), nudge_x = -rel(.2),color = "black", label=str_wrap("Monopoly Price",10), size = rel(3.5))+
scale_x_continuous(breaks=seq(0,10,1))+
scale_y_continuous(breaks=seq(0,10,1),
labels = function(x){paste("$", x, sep="")},
limits = c(0,10))+
expand_limits(x = c(0,10.5),y=c(0,10))+
labs(x = "Quantity (q)",
y = "Price (p)")+
blake_theme()+
theme(plot.margin = margin(t = .1, r = .1, b = .1, l = .1,unit= "cm"))+
NULL
mp2
ggsave("graph_mp2.png",width = 10,height = 10)
dwl_neg<-tribble(
~x, ~y,
6,6,
5, 5,
6, 4
)
ext<-
ggplot()+
geom_polygon(data = dwl_neg,
aes(x = x,
y = y),
fill = "black",
alpha = 0.3)+
geom_text_repel(aes(x=5.5,y=5),label=str_wrap("Welfare loss from pollution",10),
nudge_y = 2.1,
nudge_x = -1,
direction = "x",
vjust = 0,
segment.size = 0.2
)+
stat_function(fun=demand_1, geom="line", size=2, color = "blue")+
geom_label(aes(x=10,y=demand_1(10),hjust=0.5), nudge_x = rel(.5), color = "blue", label=str_wrap("Marginal Social Benefit",10), size = rel(3.5))+
geom_segment(aes(x=0, xend=5, y=5, yend=5), size=1, linetype="dotted")+
geom_segment(aes(x=5, xend=5, y=0, yend=5), size=1, linetype="dotted")+
geom_label(aes(x=5,y=0,hjust=.5),nudge_y =+rel(.5), nudge_x = -rel(.5), color = "blue", label=str_wrap("Optimal quantity with all costs internal",10), size = rel(3.5))+
geom_label(aes(x=0,y=5,hjust=.5), nudge_x = -rel(.2), color = "blue", label=str_wrap("Optimal Market Price",10), size = rel(3.5))+
stat_function(fun=supply_1, geom="line", size=2, color = "firebrick")+
geom_label(aes(x=10,y=supply_1(10),hjust=.5), nudge_x = rel(.5), color = "firebrick", label=str_wrap("Marginal Social Cost incl. Pollution",10), size = rel(3.5))+
stat_function(fun=mpc, linetype="dashed", size=2, color = "blue")+
geom_label(aes(x=10,y=mpc(10),hjust=.5),nudge_x = rel(.5),nudge_y = -rel(.5), color = "blue", label=str_wrap("Marginal Private Cost",10), size = rel(3.5))+
geom_segment(aes(x=0, xend=6, y=demand_1(6), yend=demand_1(6)), size=1, linetype="dotted",color="black")+
geom_segment(aes(x=0, xend=6, y=supply_1(6), yend=supply_1(6)), size=1, linetype="dotted",color="black")+
geom_segment(aes(x=6, xend=6, y=0, yend=supply_1(6)), size=1, linetype="dotted",color="black")+
geom_label(aes(x=6,y=0,hjust=.5), nudge_x =+rel(.5),nudge_y =+rel(.5), color = "black", label=str_wrap("Quantity with external pollution costs",10), size = rel(3.5))+
geom_label(aes(x=0,y=supply_1(6),hjust=.5), nudge_x = -rel(.2),color = "black", label=str_wrap("Actual social cost",10), size = rel(3.5))+
geom_label(aes(x=0,y=demand_1(6),hjust=.5), nudge_x = -rel(.2),color = "black", label=str_wrap("Actual market price",10), size = rel(3.5))+
scale_x_continuous(breaks=seq(0,10,1))+
scale_y_continuous(breaks=seq(0,10,1),
labels = function(x){paste("$", x, sep="")},
limits = c(0,10)
)+
expand_limits(x = c(0,10.5),y=c(0,10.5))+
labs(x = "Quantity (q)",
y = "Price (p)")+
blake_theme()+
theme(plot.margin = margin(t = .1, r = .1, b = .1, l = .1,unit= "cm"))+
NULL
ext
ggsave("graph_ext.png",width = 10,height = 10)