How to Calculate Consumer Surplus and Producer Surplus with a Price Ceiling
And this tutorial men talk about consumer surplus and producer surplus, I am talk about price ceilings, I am gonna calculate total benefit before and after a pricing. As usual put price along the vertical axis in quantity along the horizontal axis, gonna put in a supply curve in the demand curve, equilibrium is right there with their daughters and also that is a price I am 8 in quantity of 6. Where they get a and six I just made it up for this example consumer surplus is area but price and below the demand curve or the area outlined their in the yellow triangle, so the blue triangle is consumer surplus, so consumer surplus is the area of the triangle which is 1/2 based times the height the basis six so you have 1/2 time six times a height, which is 20 minus 8 or 12. That 20 and that 8 20 minus 8 is 12, 6 times 12 is 72, 1/2 time 72 is 36, consumer surplus is 36 in this case which is the area of the triangle.
Producer surplus is area below the price and above the supply curve outlined in yellow or the red triangle, producer surplus is the red area there it is 1/2 times the base times height the basis six, so I have 1/2 time six times the height and height is also six. Eight menus 2 is equal 6 and that 8 there and that 2 here, so I have 1/2 times 36 which is 18 so producer surplus in this case is equal to 18. Again produce a surplus is 18 and consumer surplus is 36 benefit is 36 plus 18 which is equal to 54 that is total benefit, which is consumer surplus close producer surplus and that’s our total benefits.
All draw any price even have six dollars right there is where price ceiling quantity demanded is 7 in quantity supplied their is 4, quantity demand is greater than quantity supplied there’s a shortage and we can talk like that 27 -4 which is equal to 3 to have a shortage of three units. Producer surplus shrinks to the new level here hopefully shrink right there, it is the area below the price above the supply curve since less is consumed as consume that a quantity supply level all drawn the Green Line consumer surplus also changers and it becomes at triangle plus plus this rectangle.
To calculate consumer surplus a better take the area the rectangle plus the area of the triangle and add those two together and these two combined our consumer surplus, so the area of the rectangle is the base times height with the bases 4, which is that distance here show you still for kinda slowly but it is 4. It also has a height of 6 so the area becomes 4 times 6, four-time 6 to become involved right now four times 6 which is 24.
The area that part a consumer surplus is 24 area of the triangle is going to be a base a 4 as well for and a height of a base a 4 you stick with that for now, right there it is the base and height of 8 20 -12 there’s 8. So becomes 4 times eight 1/2 base times height which is 4 which is the base times the height of 8, which is 1/2 times 32 and that equates to 16 so the area of the triangle is 16.
Consumer surplus is the 16 plus the 24 and this adds up to 40 so consumer surplus is forty, producer surplus becomes earlier the red triangle which is still the area below the price and above the supply curve. It 4 times 4 at six -2 is equal to 4 so producer surplus becomes 1/2 times four times for 16 and this equates to a so producer surplus is 8. So it becomes total benefit is 40 plus 8 is equal 48 and this is after pricing total benefit before Super 54 total benefit, after price ceiling is 48 so the deadweight loss 6.
Was a net loss up six basically we call it that way cost and that is it area right there the gray, you are such a triangle so the area up the triangle 6, I could have also calculated the area of the two triangles are by separate but a line right there the area the top trend would be 4 and the area the bottom train would be 2 a course those two and two together. Equal 6 could have done it that way as well either way works 12 you might want to just watch this again ample compare consumer surplus before and after and also producer surplus before and after and see who are the winners and the losers.