00:01
We wish to find the consumer surplus and the critters to surplus at the equilibrium price level for these two given curves.
00:08
So the first thing we need to do is find what this equilibrium price level is.
00:13
So we do that by equating our supply curve and our demand curve.
00:19
So we get 25 minus 0 .004 x squared is equal to 5 plus 0 .004 x squared.
00:31
So now combining like turn, moving everything to one side, we get 20 is equal to 0 .008 x squared.
00:44
Dividing both sides by 0 .008 and we get x squared is equal to 2 ,500.
00:55
Okay.
00:56
So now we would only take the positive value for x because it doesn't make sense for the demand for the quantity.
01:04
To be negative.
01:06
So therefore x is equal to 50.
01:10
And this x is actually x bar because it's the equilibrium price quantity.
01:16
So now that we have x bar, we can substitute it into either the demand equation or the supply equation to find the equilibrium price.
01:25
So p bar is going to be equal to, let's say we put it into the supply equation, that would be 5 plus 0 .0 0 .04 times 50 squared.
01:40
Okay, so then putting that into your calculator and you should get p bar is equal to 15.
01:50
So now that we have x bar and p bar, we can go ahead and find our consumer and producer surplus.
01:56
So consumer surplus, c, is equal to the integral from 0 to x bar, which is 50, of our demand curve.
02:07
So that would be 25 minus 0 .1.
02:09
0 .004 x squared.
02:12
And then we have to subtract p bar times x bar.
02:16
So 50 times 15.
02:20
And now the entity derivative is 25x minus 0 .004 over 3 x cubed.
02:30
And we're evaluating this from 0 to 50.
02:33
And then we're subtracting our x bar times p bar.
02:39
Okay.
02:40
So now let's put the numbers in.
02:42
That's 20...