Perfectly elastic supply, an example

This post is going to go over the economics of perfectly elastic supply and how to find equilibrium price and quantity as well as consumer surplus when we are given a perfectly elastic supply curve. First, if supply is perfectly price elastic, then it means that any change in price will cause an infinite amount of change in quantity. This is a little unrealistic, however, imagine that you are selling pictures you created. If it costs you $5 (in printing costs and time) to produce one picture, you would be willing to sell as many as you could for $5, however you would NOT be willing to sell any for less than this price. Additionally, if people offered you more than $5, you would be willing to sell an infinite amount (time permitting). This means that you are perfectly price elastic at the $5 mark, and any change in price will cause you to produce nothing or infinity depending on the direction of the price change. This results in a horizontal supply curve.

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.

We can plug in our price of $50 into our demand function to find that quantity will be equal to 750. We can now 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.
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