How to Calculate Producer Surplus and Consumer Surplus from Supply and Demand Equations | Think Econ — Transcript

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1. 0:00Hey everyone and welcome back to the  channel. In this video we'll be learning
2. 0:03how to calculate the consumer surplus and  the producer surplus from scratch, step by
3. 0:08step using nothing but the supply and demand  equations. With that said let's get into it!
4. 0:18So as promised we'll be doing this step by step  and so we're starting literally with nothing on
5. 0:23our page. The first thing that you should do  when trying to calculate consumer and producer
6. 0:28surplus is to draw a general supply and demand  graph starting with the axis and then of course
7. 0:33we'll include a general supply and demand curve  but we don't have values for this just yet. That
8. 0:38comes after being given the equations. However  we can still label our generalized graph and it
9. 0:44looks something like this. So I've just labeled  my P* Q* the two axes and my two curves. Now
10. 0:50that I've drawn this general supply and demand  graph out I'm now ready for my supply and demand
11. 0:55equations to come into play. So let's take a look  at them. The supply and demand equations are as
12. 0:59follows. The demand equation, quantity demanded  is equal to 270 minus 5P and the supply equation
13. 1:06is quantity supplied is equal to 10P. So now  that we have our demand and supply equation
14. 1:12we're going to take note of them and we're going  to use them to calculate four key points on this
15. 1:17generalized supply and demand. The first point is  where the demand curve intersects the price axis,
16. 1:24the second point is where the supply curve  intersects the price axis, and then we have P* and
17. 1:30Q*. Once I've calculated those four points I'll be  able to calculate consumer and producer surplus.
18. 1:35Let's begin by calculating equilibrium. So if you  aren't sure how to calculate equilibrium we'll be
19. 1:41doing that in this video however if you need extra  practice we have other videos on our channel which
20. 1:46are dedicated exclusively to calculating  equilibrium price and quantity so please
21. 1:51take a look at those if you find yourself needing  more practice. However, as this is a step-by-step
22. 1:55video we'll be going over how to do that in this  video as well. So when calculating P* and Q* you
23. 2:01simply set the demand equation equal to the supply  equation and that's going to yield us 270 minus 5P
24. 2:07is equal to 10P. After some simple rearranging I  get 270 is equal to 15P and then finally isolating
25. 2:14for P, I get P* or the P value at equilibrium  is equal to 18. Now that I have P* I can sub it
26. 2:21into the quantity demanded or quantity supplied  equation. I'm going to use the supply equation
27. 2:27because it's significantly easier however no  matter which one I sub it into it's going to
28. 2:31give me the same value for Q. So subbing it into  the supply equation I get Q* or Q at equilibrium
29. 2:38is equal to 10 times our new price which is 18.  10 times 18 is 180 and therefore I now have my
30. 2:45Q* which is 180. P* is 18 and Q* is 180. So let  me transfer those values onto my graph. Now that
31. 2:54they're labeled on my graph instead of Q* and  P* I actually have their values I'm looking for
32. 2:59two more points. That is where the demand curve  intersects the price axis and where the supply
33. 3:04curve intersects the price axis. So these are the  last two points I need to calculate consumer and
34. 3:08produce surplus. So how do I do that again? Well  anywhere along the price axis we know that the
35. 3:14quantity is zero. That is, for y-intercept the  x value must be zero. So all I need to do for
36. 3:21each equation is set quantity equal to 0 and  solve for P and that's going to give me my P
37. 3:26intercept or my y-intercept in this case. Let's  start with the demand equation which will yield
38. 3:31us the price intercept for the demand curve. So  subbing in 0 for Q I get 0 is equal to 270 minus
39. 3:395P. Rearranging I get 5P is equal to 270 and then  finally isolating for P I get a P value of 54.
40. 3:49So that is my P intercept for the demand curve.  Doing the same thing for the supply equation
41. 3:55I get 0 is equal to 10 P. Well this one's even  easier. P must be equal to zero as well. Now that
42. 4:03I have my P intercepts for the supply and demand  curves I can now label those on the graph as well.
43. 4:11So now that everything's labeled we're on to our  final step and that is actually using these four
44. 4:16points to calculate consumer surplus and producer  surplus. As for the supply and demand equations
45. 4:22well now that we've used them to calculate these  four values we no longer need them anymore so
46. 4:26let's get rid of them. Now remember consumer  surplus is the area below the demand curve and
47. 4:32above the market price and producer surplus is the  area above the supply curve and below the market
48. 4:39price. So all I need to do is calculate the area  of these two triangles. So let me center out this
49. 4:45graph in the middle and we'll start solving.  The area of a triangle is simply equal to
50. 4:50base times height divided by two. We'll start by  calculating consumer surplus or the green triangle
51. 4:56here. The base is 180 and the height is 36. The  height in this case is simply the difference
52. 5:03between 54 and 18 which is 36. So if the area of  the triangle is base times height divided by 2
53. 5:11then consumer surplus must be 180 times 36 divided  by 2. And this yields as a result of 3240 dollars.
54. 5:21Now we're going to do the exact same thing except  for the pink triangle and you'll notice that now
55. 5:26the base is still 180 but the height is 18, and  that's simply the difference between 18 and 0. So
56. 5:34if the area of a triangle is base times height  divided by 2 then producer surplus must be 180
57. 5:40times 18 divided by 2 and this yields me a result  of 1620. And just like that I've calculated both
58. 5:48my consumer surplus and my producer surplus using  absolutely nothing but the supply and demand
59. 5:54equations. I hope you found this video useful  and if you did let us know by liking the video,
60. 5:59subscribing to the channel, and comment down below  what sort of economic topics you'd like to see
61. 6:03us cover in the future. Thanks for watching  this video and we'll catch you in the next!