00:01
Hi, here we have a producer surplus problem.
00:06
We have that p is in dollars and x is number of units.
00:10
We have that the supply function is given by this 4x square plus 6x plus 5.
00:16
The equilibrium price is 383 per unit.
00:20
What is the producer's surplus? so here this is the setup of the problem.
00:26
We have that this is the supply function.
00:30
P of x equals 4x square minus 6x plus 5 we call pe this is the equilibrium price and in order to find either consumers are plus or producers are plus we actually need to also know what is the equilibrium quantity which i'm going to denote by xe here so we are looking first for the equilibrium quantity to find the equilibrium quantity, we are going to use this equation and we are going to set this equal to the equilibrium price so that we will find the corresponding equilibrium quantity.
01:13
So at the equilibrium price is going to be achieved at the equilibrium quantity and we are looking for that.
01:23
So we have here a quadratic equation to solve.
01:26
That means we have 4x square minus 6x plus 5 minus 383 is equal to 0, which gives us 4x2 minus 6x.
01:39
Actually, this is plus.
01:41
I don't know why i put minus here.
01:44
This is plus.
01:45
Okay, 4x square plus.
01:48
We have plus here...