00:01
So in this problem, we're told that the price elasticity of demand for a linear demand function, which is d of p, whoop, i should probably should have written that down.
00:07
So d of p is equal to b minus a, p, is given by the equation for q.
00:13
So in part a, what we're being asked to do is to rewrite the formula to express the price as a function of elasticity.
00:21
So in other words, we need to find p, and we're going to call this q of, or g of q.
00:27
So in other words, we're going to take this original equation, and we're going to solve it for p.
00:31
So if i go to the side, i'm going to have q equals a times p divided by b minus ap.
00:37
So we're going to solve this first.
00:39
So the first thing we need to do is remove or get rid of our denominator by multiplying both sides by b minus ap.
00:45
Because on the right hand side, they'll cancel off, and on the left we'll distribute.
00:49
B times q is bq.
00:51
Let's make it a capital there.
00:53
And negative ap times q is negative apq.
00:56
And this is all equal to ap.
00:58
Well, my goal is to isolate is to isolate p.
01:02
So what i'm going to do is i'm going to add the apq to both sides of our equation.
01:07
So now we're going to have bq equal to ap plus apq.
01:13
Now, because we're trying to isolate p, both terms contain the p.
01:17
So i'm going to factor out that p, which leaves us with p times a plus a times q.
01:23
So now we can go ahead and solve for p by dividing both size of our equation by a plus a times q.
01:32
So if i scroll up a little bit, so you can have some room.
01:35
So now we'll find that bq divided by a plus a q is equal to p.
01:40
So perfect.
01:40
Now we've found our equation...