All goods and services are subject to scarcity at some level. Scarcity means that society must develop some allocation mechanism – rules to determine who gets what. Over recorded history, these allocation rules were usually command based – the king or the emperor would decide. In contemporary times, most countries have turned to market based allocation systems. In markets, prices act as rationing devices, encouraging or discouraging production and encouraging or discouraging consumption in such a way as to find an equilibrium allocation of resources. We will construct demand curves to capture consumer behavior and supply curves to capture producer behavior. The resulting equilibrium price “rations” the scarce commodity. Markets are frequent targets of government intervention. This intervention can be direct control of prices or it could be indirect price pressure through the imposition of taxes or subsidies. Both forms of intervention are impacted by elasticity of demand. After this course, you will be able to: • Describe consumer behavior as captured by the demand curve. • Describe producer behavior as captured by the supply curve. • Explain equilibrium in a market. • Explain the impact of taxes and price controls on market equilibrium. • Explain elasticity of demand. • Describe cost theory and how firms optimize given the constraints of their own costs and an exogenously given price. This course is part of the iMBA offered by the University of Illinois, a flexible, fully-accredited online MBA at an incredibly competitive price. For more information, please see the Resource page in this course and onlinemba.illinois.edu.
3-2.3. Derive Short Run Average Cost Family of Curves
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Del curso dictado por University of Illinois at Urbana-Champaign
Firm Level Economics: Consumer and Producer Behavior
416 calificaciones
University of Illinois at Urbana-Champaign
416 calificaciones
Curso 1 de 7 en SpecializationManagerial Economics and Business Analysis
De la lección
Module 3: Firms, Production, and Costs
This module will introduce cost theory. Firms are interested in producing profits, which are the residuals when costs are subtracted from revenue. Earlier modules constructed demand curves. They give us an idea of how many units of product we can sell at different prices; this would be firm revenue. We will work to understand inputs, production, and costs.
Conoce a los instructores
Larry DeBrockDean Emeritus and Professor of Finance and Professor of Economics
University of Illinois, Urbana-Champaign College of Business Department of Business Administration
[SOUND]
[SOUND] In
this lesson we're constructing cost curves.
And previously we looked at how to build a total cost curve.
We got that information by understanding the production function,
translating that production and function and
the inputs that it entails, into dollars and figures of expenses.
And we were able to build a total cost curve.
In this video, we're gonna think about building a new type of cost curve.
So we'll start with a definition, and
we're gonna define something called average cost.
It's really average cost but we'll be a little bit formal and say average total
cost, which we will start using the shorthand of ATC for average total cost.
And average total cost is just basically per unit cost.
That's the way to think about average total cost.
It's defined as the ratio of total cost to output.
So, if you think about our ongoing example of
the mayonnaise at the Kraft plant, there's
a total cost to run that plant and Kraft's accountants can figure that all out.
You add up everything that's involved.
That just the labor, the cost for the brick and mortar, the cost for the eggs,
the cost for the glass, the cost for the design team and the focus
groups to look at the labeling to see what they wanna put on the side of the jars.
All of these things are all involved and if you take all of those costs and
divide them by the total amount of jars of mayonnaise that went out, what you've got
is the prorated share of cost that belongs to each one of those jars of mayonnaise.
Each jar of mayonnaise, say has, if you take the total cost and
divide it by the number of mayonnaise, maybe $3.28 of cost.
That's the per unit cost.
It's gonna be important to us, because as you can imagine,
if I tell you that the per unit cost of $3.28, but the price that the market
will support is $3.18, eh, it's probably not a good market to be in.
At that point in time, you begin to realize, well, I'm not making as much back
as I actually put into each one of those jars of mayonnaise.
So, we're gonna have to know a lot about this average cost when we start thinking
about why firms exist, what they're doing with their line of business.
So I'm gonna expand this a bit,
talk about it a little bit more in terms of what's going on.
We know in fact I can rewrite this numerator as fixed
cost plus variable cost over output.
And I can expand that out to the term of fixed cost
over output plus variable cost over output.
And this term we're gonna relabel as average fixed cost, and on this term,
we're gonna relabel as average variable cost, otherwise know as AFC or AVC.
And I'll just rewrite these, then, as average total cost is equal to the sum
of average fixed cost plus average variable cost.
Just as we did when we built the total cost curve,
we built the total cost curve by looking at the two components of it.
The fixed cost component, we drew a graph for that.
The variable cost component, we drew a graph for that.
And then we added the two to get the total.
We're gonna do the same strategy here.
I wanna get to this.
Average total cost.
I'm gonna build this and add that after I build it, okay?
So, let's start.
And what I'm interested is figuring out what does the average
fixed cost curve look like?
Well, average fixed cost is definitionally,
Equal to fixed cost divided by output.
We saw that on the previous slide.
Average fixed cost is just fixed cost divided by output.
So on this slide we want to understand what that picture looks like.
Well, immediately you could see since the numerator is fixed as I step along
this axis to the right increasing output this denominator is going to grow and
this numerator is constant which means this has to be a falling curve,
in fact it falls in a very specific way.
It's not a straight line at all.
It's a curve that looks like this.
We'll call this curve average fixed cost.
Think about it.
As output gets very large, let's go back to this picture, this ratio.
As output gets very large, what's happening to this ratio?
It's getting very small but does it ever get to zero?
No.
It asymptotically approaches the horizontal axis.
But it's never really gonna touch the horizontal axis which would be zero level.
Likewise, if output got very small, and as you start reducing production a lot,
this thing would go up very, very fast in a hurry.
In fact if it went to zero, this thing would not be defined.
It would just, it's infinite.
Think about it, suppose I tell you that if you're gonna sell cars
you gotta put advertisements on TV.
Well, advertisements on TV cost a lot of money.
If you got a $10 million dollar ad campaign, but you sell 10 million vehicles
like a big company like General Motors, well, it's about a buck a car, okay.
But if you have to spend the same $10 million that General Motors spent
to put your ads on TV and you're only gonna sell a million cars,
the per car share of that fixed cost is now ten bucks a car.
Still not a big deal but
suppose you're sort of a boutique seller who only sells 250,000 cars.
They're expensive and part of the reason they're expensive is because when you put
the commercials on now, the per car share is pretty high, okay?
When you gotta start making small numbers of cars and you still try and advertise
those, that average C=cost, that average fix cost, is gonna get pretty steep,
that's what this curve reflects, in if you show this to somebody
who is in a geometry class, they'd say that that's a rectangular hyperbola.
A rectangular hyperbola is exactly this, it's a hyperbola, it's curved, but
it's curved in a special way.
If you'd have take any point on this graph, the rectangle
defined by that point would be the same area.
That area of course, as you could guess, would be that constant fixed cost.
No matter what point you pick on this graph, it will define a rectangle.
The area of that rectangle will be a constant equal to that.
All right, we're only halfway home.
Remember, we have to do this,
and we have to do this, and the second one is a little bit harder.
It was before, but we got through it and we'll get through this one.
Draw another graph, another axis system, you know we put dollars and cents on
the vertical and we put output on the horizontal, and now I want to think about
the average variable cost, which is equal to the variable cost over output.
But when I did average fixed cost, the ball game was easy.
Because as I increased my output,
the denominator went up, but the numerator was constant.
Not the case anymore.
As I increased my output, the denominator's gonna grow, but
I also know the numerator's gonna grow, cuz more output is gonna be more costly.
There's no such thing as magic production.
If I wanna put more output out there,
I know my variable costs are going to have to grow.
And so what's really interesting to me,
then, is what's happening to the rate of change of these two.
What's happening to the rate of change of these two?
And so the way I'm going to think about this
is I'm going to ask you to take a simple abstraction with me.
Let's go back and look at our variable cost curve.
The way we designed it earlier.
And we had a variable cost curve that looked like This.
Right?
And I know that what I'm looking for today is something called
the average variable cost, which would be the ratio of the numerator,
which is variable cost to the denominator, which is quantity.
Well suppose that I picked some amount here, right here.
We'll call this q sub 0.
I know that at q sub 0, variable cost would be equal to this height.
Let's call that VC at q0.
That would be the variable cost at output level q0.
But look what I'm asking.
I've been asked to evaluate a ratio that is essentially variable cost,
which is that height over output, which is that length across the horizontal axis.
But, remember your old trig days, that's opposite over adjacent.
And if you take the opposite side of a triangle over the adjacent side
of a triangle, that's going to give you essentially the slope of that line.
And as you can see, as we step out now if I were to take a different output level,
The base is the new higher output.
The denominator is the new higher cost and the triangle formed by those two,
that slope, that slope of that third line, hypotenuse, is falling.
And eventually we get out to some point like about right here where that
line will in fact just be tangent and then if we continue to increase output
We're gonna see our triangles are now going to have the third line.
The hypotenuse is now gonna start getting steeper and steeper and so
don't get too confuse enough in a trigonometry that, understand that what's
happening here is that at low levels of output as I increase my output that
Slope of that line that is the third side of a triangle is getting smaller and
smaller it's falling.
What that means is that the average variable cost is falling.
Now, it's not negative, I'm not saying it's going negative,
cuz there's no such thing as negative variable cost, right?
But, it's going down, the ratio itself is collapsing, and
that's the magic we needed, because when we were over here, looking at the picture,
we said what I need to know is somehow as I increase output,
what's happening to the relative size of the numerator and the denominator?
And now I know that the numerator and the denominator, that ratio is falling over
a certain range and then rising and economists will draw that like this.
And we'll call this average variable cost and
we call this U-shape Average Cost Curves.
Where is that shape come from?
It comes again from that idea that in the production function
there is some low levels of output where
as you increase output your costs don't increase as much as your output does.
And so the average of that variable cost function is actually falling.
That would be this region.
But after some point, that famous inflection point.
Trying to get more output gets increasingly expensive,
and we can see the average cost starts to go up.
Okay, so we've got the two curves done.
Let put them together.
We want to build an average cost.
We now know that we have an average fixed cost curve.
That looks like this.
We have an average variable cost curve that's got some general U-shape to it.
I'll just put it here.
And we'll talk more about where that general U-shape might be as we go forward.
Average variable costs.
And now I just want to add the two.
And if I add the two, it's gonna look something like this.
This is our family of average cost curves.
We had three different total costs we were looking at.
We are looking at a fixed cost curve,
a variable cost curve, and the sum of those was the total cost.
And now we have an average fixed cost curve.
We have an average variable cost curve and
the sum of those is this average total cost.
Now, it's important that we talk a bit about something that you should see here
is the fact that Larry's kind of just a sloppy draftsman, or
is there something going on here?
And in fact, there is something going on here.
So we're gonna say there's a couple regularities here.
First of all, you'll note the way I've drawn it.
The output, That minimizes
average variable cost is less than the output
that minimizes average total cost and
that is, in fact, a regularity.
It's not just Larry's sloppy drafting.
That's the way it's gonna be and has just has to do with all sorts of properties you
could prove if I gave you a cost function and you knew something about calculus you
could take that cost function, construct an average cost function which is dividing
it by two, take the derivative of that, and once you have your average cost curve
you will know exactly how to minimize that by taking the first order condition.
All those sorts of things you could do with an average variable cost, and
you could prove what I'm writing down right now, that the output,
that minimizes average variable costs, is less than the output,
it's actually less than or equal it might be equal now and then,
the output that minimizes average total cost.
The other thing is happening here is that for high output,
average variable cost and average total cost converge.
They don't quite touch but you can see that for
high output because average fix cost is vanishing, for
high output levels average fixed cost is asymptotically approaching the axis.
That means those two curves, average total cost and average variable cost are going
to be getting closer and closer as you go farther out.
So, this is our family of average cost curves.
We've got one more cost curve we need to introduce.
Actually, it's the most important one, but it builds upon these.
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