Now for our example, imagine we have a good that is at a perfectly elastic supply price of $50. We additionally have a demand curve that is linear with a slope of -0.20. We also know that none of the product will be demanded at a price of $200. We have enough information now to draw a supply and demand graph and calculate the equilibrium price and quantity.
First, we should write the associated inverse demand function, or inverse demand equation:
P = 250 - Q*.2
We plug in the values of 250 and .2 into our inverse demand equation.
To get our demand function, we have to multiply both sides by 5, add Q to both sides, and subtract 5P
This gives us our demand function as:
Q = 1000 - 5P
We now know that the demand curve will intersect the quantity axis at 1000, and since supply is ALWAYS going to be equal to $50, we can draw a horizontal supply curve at a price of $50.
calculate consumer surplus by finding the area under the demand curve buy above the price. This ends up being a triangle where the height is 150 (200-50) and the base is 750 (750-0). We multiply these two numbers and divide by 2 to get: 56,250 our consumer surplus.