00:01
In this problem we know that the supply function for oil is given by s of q equals q square plus 10 times q which is given in dollars and the demand function is d of q equals 900 minus 20 times q minus q square also given in dollars then we are going to graph both curves in part eight that is we're going to graph in the same axis the supply and the demand functions and here we have this graph here where the blue line is a supply function which shows the typical increasing behavior starting at zero in this case and the demand function is the red line with a decreasing behavior and then the there is a point where the two lines meet and that's the point of equilibrium.
01:22
The point of equilibrium is the point where the two curves meet and is what we get to find in part b.
01:31
And for that we are going to solve the equation supply of q equals demand of q.
01:39
That is the equation two square plus 10 times q equals 900 minus 10 times q minus q square then this equivalent to and then we put this turn to the left and we get two times q square then this term out also to the left we get 30 q and this term 2 to the left minus 900 equals 0 and so we have a second degree polynomial equal to 0 and we apply the formula we know very well that is q equals negative 30 more or less 30 square minus 4 times 2 times negative 900, all that over 2 times 2.
03:02
And that is negative 30, more or less, square root of 9, 900, minus or plus, because we had negative 4 or negative 900, 8 times 900, divided by 4, and that's equal to negative 30, more or less.
03:40
Square root of then we have 900 as a common factor here or better not to do that better we say that we say that we have 900 plus 8 times 900 so it's 9 times 900 390 900 as if it's were an object or a variable and then we get negative 30 more or less square root of 8100 over 4 and the square root here and the square root here is equal to you have negative 30 more or less the square root which is 90 over 4 and so we have two possible solutions x1 we're going to call the solution obtained by taking the negative sign in this equation and we know that this is this result here is negative so it's not valid because x represents if i said q i want to say because it's q here because we are talking about q so it's q1 and this is not valid because q is a quantity so the quantity of a product so it's a positive or no and the other option is negative 30 plus 90 over 4 and that's 60 over 4 which is 15.
05:42
So the quantity of equilibrium is 2 star equal 15.
06:03
With that we are now going to calculate the price associated to this equilibrium quantity...