Our goal as you know,
is to figure out equilibrium in this market,
a perfectly competitive market.
The conditions of perfect competition have led us to
understand that perfectly competitive firms treat price as given.
Now, what we want to do,
is think about supply.
That's what we're trying in constructing.
We built demand a long time ago.
We're trying to think about a supply curve in this industry,
and here's what we're going to do.
We're going to build a supply curve for a particular firm first,
and then, we'll aggregate up,
because we've got lots of these firms.
So, our goal is to derive
a supply function for a single firm that's in a competitive market,
and for us, just to be clear,
we're calling it a perfectly competitive industry.
Once we know that, we can aggregate up.
Now, again, we'll start with some notation.
We're going to let lowercase q sub i be defined as the individual output of firm i,
and we're going to let capital Q be defined as market output of all firms.
What that means, is that I know my graph output then,
is just going to be equal to the summation for i equals one to n,
where there are n players in
this industry of the individual outputs of each of these firms.
Where do these outputs come from?
That's what we're doing, we're to build a supply curve to show
the optimal response of an individual player.
Once I figure out the response function for an individual player,
then I'm going to sum across these response functions and I have a market supply curve.
Alright. So, let's recall that for profit maximization,
we wanted to set marginal revenue equal to marginal cost.
That is, the individual firm which search for the output level,
firm has no control over price, price is given.
With such for the output level,
where the marginal revenue of the last unit produced,
is just equal to the marginal cost of the last unit produced.
Graphically, we put dollars and cents,
or price, in the vertical axis.
On the horizontal axis,
we'll put lowercase q,
representing the individual firm,
and we know the marginal cost curve for that firm looks something like this.
Now remember, the marginal cost was actually U-shaped when we built the cost curves,
but we were able to determine earlier that for any parametrically given price,
the firm doesn't really care about
the downward sloping part of the marginal cost curve of the firm,
the action happens where the marginal cost curve is sloping up.
So, this curve really does have this part here,
but I'm just not really showing it going forward.
So, we'll go forward and just take
these off here just to get the clutter factor a little bit reduced.
Marginal cost remember, was the slope of the total cost function.
The derivative of cost,
the change in cost for a change in output,
and we want to set that equal to marginal revenue
for a firm in a perfectly competitive market,
we know that a firm faces a price from the market,
some price p zero,
and that is in fact,
the marginal revenue for the firm.
How do we know that? Well, we establish that they are price takers.
For every given unit of production,
they get exactly price.
Think about, you could say,
''Well, how's that work?''
I hope, I guarantee,
take the largest corn farmer in Illinois,
the largest corn farmer in Illinois,
and have her double her production.
It's the largest corn farmer doubled her production,
what will be the impact on the price of the Chicago Board of Trade?
Nothing. Be like a little bug landing on a lake,
that ripple effect would be smaller.
Now, if Honda were to double its production of a chords,
there would be some impact on market prices,
but that's a different game.
That's what we're going to talk about later.
When there's a small number of producers,
their output decisions can actually have big impact.
Here, we're talking about a special case where firms are
relatively so small that their output decision doesn't impact price.
So, for this particular farmer,
if corn is three dollars and forty cents a bushel,
for every extra bushel of corn that is walking across the horizontal axis,
the output for this particular farmer as she produced more and more corn,
every extra unit will get exactly what the market price was.
So, that's why we have that horizontal line and
we call marginal revenue, the change in ribbon.
Of course, this means for
profit maximization that the firm will want to set marginal revenue equals marginal cost,