Consumer and Producer Surplus

Calculating the Consumer Surplus as an Area

The sum of individual consumer surpluses is the total consumer surplus, shown on a graph as the area below the market demand curve and above the market price.
Consumer surplus is the difference between how much a consumer is willing to pay for something and the actual price of that thing. It can be calculated as an area. A step diagram uses horizontal lines to represent intervals (steps): a range from one point to another point. By drawing a demand curve as a step diagram, each individual's consumer surplus (the area below a consumer's willingness to pay and above the market price) is also the area of a rectangle. Total consumer surplus is the sum of all individual consumer surpluses, so it is the total area below the market demand curve and above the market price. The area of a rectangle is its base multiplied by its height. The base of Andrea's step is the additional number of cups she adds to the market (10=1)(1\;-\;0\;=\;1) . The height of her step is her willingness to pay minus the market price, which is two ($4$2=$2)(\$4\;-\;\$2\;=\;\$2) . Andrea's consumer surplus is the base of her step times the height of her step: $2×1=$2\$2\;\times\;1\;=\;\$2 . For Brett, the base of his step is also one (21=1)(2\;-\;1\;=\;1) . The height of his step is one ($3$2=$1)(\$3\;-\;\$2\;=\;\$1) . Brett's consumer surplus is $1×1=$1\$1\;\times\;1\;=\;\$1 . For Christy, her consumer surplus is $0.50×1=$0.50\$0.50\;\times\;1\;=\;\$0.50 . Adding up the area of each rectangle gives us total consumer surplus: $2+$1+$0.50=$3.50\$2\;+\;\$1\;+\;\$0.50\;=\;\$3.50 . There is no surplus for Deb, Eddie, or Frank because the market price is above their willingness to pay, so they choose not to purchase coffee.
To calculate the consumer surplus for individuals in this market, multiply the base of their step (the quantity) by the height of their step (willingness to pay minus market price). The base of each step in this case is 1 cup of coffee. Total consumer surplus in this market is the sum of the individual surpluses.
The demand curve can be drawn as a step diagram for a scenario involving only few potential consumers in the market. With a big market that has a large number of consumers in it, those individual steps will smooth out and we will have a demand curve that is a downward sloping line. Smoothing out data is done to show key patterns in data, without zeroing in on fine details. The coffee market in the United States is a big market with a large number of consumers. It is estimated that half of the US population, around 150 million people, drink coffee. Americans consume 400 million cups of coffee per day, with an average price in a coffee shop of $2.38 per cup.
The US coffee market serves around 400 million cups per day at an average price (market price) of $2.38 per cup. The consumer surplus for this market is the area below the demand curve and above the market price.
With a smoothed out demand curve because of the size of the market, the consumer surplus (the area below the demand curve and above the market price) is now the area of a triangle. More specifically, it is a right triangle, because two of the sides (the axes) form a right angle. The area of a right triangle is 12×b×h\frac12\times b\times h . Where b is the base of the triangle and h is its height, the base of the triangle is 400 million. The height of the triangle is eight. In this example, the demand curve crosses the price axis at $10.00, and the price line is at $2.38, so the height is $10.00$2.38=$7.62\$10.00\;-\;\$2.38\;=\;\$7.62 . The consumer surplus in this example is thus $1.524 billion:
12×400million×$7.62=$1.524billionperday\frac12\times400\;\mathrm{million}\;\times\;\$7.62=\$1.524\;\mathrm{billion}\;\mathrm{per}\;\mathrm{day}