# A single price monopolist is a monopolist because it is the only supplier of a particular product. The monopolist therefore has the power to choose a price to sell the product at.
# Those who have a willingness to pay which is greater than the price will buy the good while those who have a willingness to pay for the good which is less than the chosen price will not but it.
# Our monopolist is a broadband internet supplier within a city.
# For now let's say they only offer one bundle.
# Let's generate our consumers
npeep <- 2000# Number of potential consumers
wtp <- 45 + rnorm(npeep)*15# Each person has a different willingness to pay which
# To figure out the demand curve we count the number of people willing to pay at least as much as the offering price.
maxop <- 90# Max offering price op <- 0:maxop # Offering price ranges from 0 to maxop qd <- rep(NA,length(op))# Quantity demanded for(i in1:length(op)) qd[i] <- sum(wtp>=op[i])
mc <- qd*.01# Marginal cost is increasing though this is not a neccessity # For something like broadband services we might think that up to a point marginal costs might be decreasing since the cost of adding one more customer might be less than the cost of adding the previous customer.
minmax <- function(...)c(min(...),max(...)) plot(minmax(op),minmax(tr,tp), type="n", ylab="Total Revenue - Blue, Total Profit - Red", xlab="Price", main="We can see optimal pricing\nfor the monopolist is around 39 dollars") grid() abline(h=0, lwd=2) abline(v=39,col="red", lwd=2) lines(op,tr,col="blue", lwd=3) lines(op,tp,col="red", lwd=2)
# We can see at the price around 18 which would be the optimal price for the consumer, the supplier is making almost no profits.
# The last thing we might wish to consider to Total Surplus or total system efficiency which is defined as that which the consumer benefits by purchasing a good below the consumers willingness to pay plus that of the suppliers profit at that price.