00:01
During the summer months, terry makes and sells necklaces.
00:05
Last summer, she sold necklaces for $10 each, an average $20 per day.
00:15
We're ultimately going to want a demand function.
00:18
We usually do price as a function of quantity sold, so we'll let x be how many sold.
00:24
So the number sold is the input, so 20 necklaces yields an output of $10 per necklace.
00:35
And then when she increases the price by $1, so that's up to $11, the average decreased by two sales.
00:46
So it's down here to 18.
00:50
All right, so we have each increase by $1 decreases the sales by two, so that gives us our slope, but you could just do it like this as well.
01:05
You do 11 minus 10 over 18 minus 20, so that's 1 over negative 2, negative 1 half, for our slope of our demand curve.
01:22
And we can put this together in the point -slope formula.
01:28
So remember we have y minus y1 is mx minus x1, but our y's are actually prices.
01:38
So we'll do p, variable p, minus one of the prices is the slope.
01:47
X is the quantity minus one of the x's.
01:52
And the x1, p1 has to go with one of the curves.
01:56
Let's just take this one.
01:57
It'll be easy to work with.
01:58
So we have p minus $10.
02:03
Remember the output's the price.
02:04
These are in x, p pairs.
02:11
Negative 1 half x minus 20.
02:18
So solve that for p as a function of x.
02:21
We'll have negative 1 half x.
02:24
Minus minus becomes plus 10.
02:29
Negative 1 half times negative 20, plus 10.
02:32
And then when we move the 10 over from the other side, we end up with plus 20.
02:37
So we can double -check that it fits our data.
02:39
If we have x equals 20, negative 1 half times 20 is negative 10, plus 20 is indeed 10.
02:49
And then if we have x is 18, negative 1 half times 18 is negative 9.
02:58
Negative 9 plus 20 is 11.
03:02
So it works out.
03:03
There's our demand function...