So, why do users want to consume exactly at their demand curve?
Well, in order to understand this, we'll just logically consider two different
cases. And you'll see exactly at the end of
this, why it is that you want to consume exactly what your demand is.
so, first case, suppose we consume less than our demand.
So, on the demand curve right here, this price per unit.
So, suppose that you dro, you drop the quantity you consume down maybe to here.
So, it's below your demand curve now. Say okay, well, we're just going to
consume right at this quantity. Okay.
So, now if we draw this line up in here. We'll just draw all the way out to the
end. You'll just see in a second,
Now, the, the amount that you have to pay has now decreased, right?
So, because you're happened to have this quantity where you're down at this
quantity, right? So, at the same price per unit, you're
consuming less amount and the amount that you have to pay is going from this
quantity times this price per unit times whatever this quantity is times this
price per unit, right? So, the decrease is from here times here
to here times here. And so, it's really decreasing by this
area in here, right. This is the decrease, so, we can call
that B1, [INAUDIBLE]. But now that you're, you know, dropping
down the amount you're consuming, the utility is going to drop too, right.
So, the utility is also going to decrease in addition to the price decreasing.
So, you just saw the price decreases by B1.
And the utility though, remember the utility is everything to the right of the
demand curve. So, it's everything in this way, that's
the utility. So, the utility is going to drop by the
entire area in here. Right.
So, this entire area. That's how much the utility is going to
drop. So, it is we call this A1 can, with her
convetion before staying the same, the utility is going to increase, decrease by
A1 plus B1. So, if you remember the net utility was
the total utility minus the price. So, now we have on this one side total
utility minus the price that you're going to have to pay.
So, we want the price to be lower and the utility to be higher.
But the problem is that the utility is decreasing by A1 plus B1 and the price is
decreasing by only B1, right? So, we're actually losing now, so, I'll
write this as a negative A1 total here. So, we're actually going to have a lower
net utility than we could have had if we had stuck with just our quantity.
So, if we'd, if we'd consumed exactly at the quantity, we would have had an extra
A1 of utility. So, we've, we've just gone down.
Now, in second case we're going to consider is, what if we consumed more
than our demand. So, in the opposite sense now, okay,
well. Okay, now you've convinced me why I don't
want to decrease the quantity that I've purchased, because my utility is going to
go down. But what if we consume more than our
demand? Well, now okay.
So, say then, you increase the amount that you're going to consume up to here.
Okay. And I'll draw this line again, at this
pointer right, right over here. So, now, th, the the amount that you're
going to have to pay is increasing, right?
But remember, we're still at this price per unit, right?
So, the amount you're going to have to pay is this rectangle.
And this this price per unit, at this quantity, where to this is the amount
you're going to have pay. It just went up by this entire area in
here. That's how much it went up.
Okay? And so, we'll call this again, we'll call
this B2 this time, because it's not the same as B1.
And we'll call this A2 in here, this guy A2, B2 and A2.
So, your utility is increasing, oh, sorry, sorry, your price is increasing by
A2 plus B2, right. And now, your utility remember is
everything to the right of the demand curve, right?
So, you're, you're utility is this area in here, is B2.
Okay? So, your utility is going up by B2, and
your price is going up by A2 plus B2. Okay?
So, now, again you're losing out because your, your added utility is not
counteracting your added price. Right?
So, you're really losing out now if you do total utility minus price again.
You're going to have a negative outcome, right?
because you're going to be paying more, and it's going to be negative A2 in here.
So, again, you're losing. You're losing out, and in either case,
you see you're going to have a negative result, right?
So, you're going to lose money, basically.
You're or, not money necessarily, but we can quantify it all in terms of money.
But you're going to lose net utility. So your net utility is going to go down.
And so, therefore the conclusion is that the demand curve itself maximizes the net
utility. So, consuming exactly at your demand is
going to maximize the net utility. Okay.
because if you go lower, it's going to go down and if you go up, it's also going to
go down. So, demand curve is maximizing net
utility logically.
Christopher BrintonLecturer
Mung ChiangProfessor
