00:01
So here we're given a demand curve, a supply curve, and a price ceiling.
00:04
It's a little bit unclear the way the question is done, but i think in the first situation, they're asking us to find the equilibrium that would prevail if no price ceiling existed, right? so here the demand curve starts at 97 and slopes down.
00:23
The supply curve starts at 25 and the supply curve slopes up.
00:30
Missed a sign there.
00:33
And that leads to some equilibrium here.
00:35
How do we find that equilibrium? well, we equate demand and supply, which is what i'll do in a, right? demand is equal to supply.
00:43
That gives me 97 minus x is equal to 25 plus 0 .8x, which gives me 72 equals 1 .8x, which gives me an x quality of a joint.
01:00
Joining to the calculator.
01:01
Again, this is listed as a calculus question, but i don't think there's any reason to do calculus here.
01:08
X equals to 40, which would give you a corresponding price of 97 minus 40 equals to 57, right? if i plugged this back into the supply equation, i would get the same thing, but it just seemed easier to put it back into the demand.
01:28
So the initial free market equilibrium has a price of 57, diagram obviously not to scale, and a quantity of 40.
01:38
Great.
01:39
Now, the question is at b, we can now see that the price ceiling of 45 is actually going to be binding, right? the market is not actually going to get to equilibrium, and that means the constraint here is the supply curve, right? there's going to be excess demand over supply.
01:59
So the supply that's going to pin down the equilibrium under the price ceiling is the supply curve, right? so i'm going to calculate supply of 45, which is equal to 25 plus 0 .8 times 45, right? again, a little calculator work, 25 plus 36 equals to, oh, sorry, i subbed in for the wrong thing, viaculpa, right? i'm setting supply equal to 45, not subbing in for quantity.
02:40
Long day, you probably know the feeling.
02:44
Forty -five equals to 25 plus 0 .8x, 20 is equal to 0 .8x, x is equal to 0 .8x, x is equal two should be 25 right i'm not taking any more chances with this one um 25 right exactly because i knew that the quantity right just this is one of the great virtues of graphing things is that you can tell which side you are on i knew the quantity had to be um less uh less than than 40 right so see we're now asked for the new consumer surplus right so see the new consumer surplus right so is going to be defined by this area here, right, which is a quadrilateral.
03:33
So what i need to do is i need to find this point here as well to split the consumer surplus into two parts so that i can calculate it as the sum of a triangle plus a rectangle, right? so what does that do? i need to plug in 25 into the demand curve.
03:52
So the demand of 25, is equal to 97 minus 25, which is equal to 72, right? so now i can calculate the consumer surplus is equal to the box, which is 72 minus 45 high, and it's 25 wide, plus it's a half of 97 minus 72, which is the height of the triangle, the base of the triangle is again 25.
04:21
So now again more calculated work.
04:24
They've made the numbers, i don't know, moderately easy for us...