00:01
Here we determine the consumer surplus at the equilibrium price using the demand and supply function.
00:07
So to determine the consumer surplus, first we have to determine the equilibrium quantity.
00:19
And we determine this by setting up the demand and supply equal, which means this demand function equals the supply function at the equilibrium quantity.
00:33
So therefore we substitute the demand function which is 60 minus x squared.
00:37
Equals the supply function that is 6 plus x squared divided by 2 we solve for the quantity x from this equation i subtract 6 from both sides and add x squared on both sides so this will be 60 minus 6 and this equals adding x squared to both sides we get x squared plus x squared by 2 60 minus 6 equals 54 and this equals x squared plus half of x squared will be three half x squared so let's solve for x and x from this equation by multiplying by two first and then dividing by three so we will have a 108 divided by three equals x squared so this gives x squared equals 36 now take a square root on both side to get x.
01:34
So x will be plus or minus six.
01:37
Since the x represents the quantity, we take only the positive number that is x equals six.
01:44
So this is the equilibrium quantity.
01:47
Let's see this one is qe.
01:51
Now we have to determine the equilibrium price, which we can find by substituting this equilibrium quality either into demand or into the supply function.
02:02
So let's substitute into the demand function.
02:05
We have the demand function d of x and this equals 60 minus x squared.
02:14
Substituting 6 into x we get 60 minus 6 squared.
02:21
This equals 60 minus 36.
02:25
This equals 24.
02:27
So this 24 represents the equilibrium price.
02:30
We say this is p of e.
02:36
So now that we have determined the equilibrium quantity and equilibrium price, we can write the formula for consumer surplus to determine the consumer surplus...