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.

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Module 4: Firm Behavior

The firm goal of profit maximization requires an understanding of costs and revenues. In this module, we will see how a firm optimally responds to a given market price by finding the profit maximizing output. The level of profits at this maximum profit point will help determine short run equilibrium.

Dean Emeritus and Professor of Finance and Professor of Economics University of Illinois, Urbana-Champaign College of Business Department of Business Administration

Previously, we were able to figure out the firm's optimization

behavior in a world where the firm knew its cost and

the firm face to the exogenous price, which we just labeled piece of zero.

So, the price that's give to the firm, and giving that signal that comes into

the firm, the firm knows its production technology, it's cost.

We figured out how to optimize by looking at a total revenue and

a total cost function.

And in fact, I'm gonna repeat that because we're going to find a quicker way to

doing this, but I wanna sort of draw where we were at the end of that.

We had a situation, dollar and

cents on a vertical axis, quantity on a horizontal axis.

And we had a situation where we had a fixed cost,

we had a total cost curve, and we had a total revenue curve.

And we understood that we could find the maximum profit by getting an eyeball,

or I could draw the profit function there.

But I'll just sort of eyeball it right now.

The maximum profit would be about right there, the biggest vertical gap.

Now, let's first remember a couple things.

One is that the slope of total cost is equal to the marginal cost.

And the slope of total revenue is equal to marginal revenue.

Now, vertically, you can see that gap looks to be the largest between there.

But I wanna think about this more systematically.

If you were to think about back to the days,

I'll put another one of those bubbles that's kind of a bubble that pops up

over your head in the cartoons when you're thinking about something.

Well, recall from the days that you took geometry on some axis system.

Instructor said, look, suppose we have two functions.

We have one function that says, y=f(x).

And we have another function that says, y=h(x).

Those are just two arbitrary functions I just drew.

And if your instructor said,

hey, what x level would maximize the difference between those two?

You were able to prove that the x level that you would choose,

that is, what level of x would maximize this vertical gap,

is the one where the slope of the two functions were the same.

I'll think about it.

If the slops of the two functions are different,

suppose their different like this, there's only two ways they can be different.

They can be divergent.

If their diverging, that means you still haven't found the max between the two.

So, you're not there yet.

Just keep increasing x because that gap is getting larger.

If they're converging, it means you've gone too far.

Hey, wait a minute. That gap is getting smaller.

There's only two ways that the slopes can be different.

They're either different like this or different like this.

Either one of those cases, you're in the wrong space.

Only when the slopes are identically equal to be found that max.

If you think about the story from this picture, as you start out from this

point which we'll call, we'll take this point here and call it alpha.

Alpha, the slopes are wildly apart.

And as you step to the right increasing x, the slopes are getting further and

further apart, but they're bending.

At one point the slops get to be identically equal to, and

you've got the biggest gap now.

Cuz if you go one step farther, they're actually getting closer.

So, what that means is, to maximize this difference,

you just wanna set the slopes to be equal.

Well, that's all we have to do back on this picture.

If I wanna maximize the gap between those two curves, they're just two curves.

One of them you call f of x, and one you could call h of x.

Or in this case, f of q and h of q.

I wanna find the output point where the slopes of those two are equal.

So, we will maximize profits by setting the slope of the cost function equal

to the slope of the revenue function, or marginal cost equals marginal revenue.

Now, that may have been too far back in your memory when you took your analytical

geometry class to think that through, but I hope you understand the intuition here.

If the slopes are different and they're diverging,

you still haven't found the maximum distance.

If the slopes are different and they're converging,

you're gone past the place where the two curves are farthest apart from each other.

Only when the two slopes are equal.

I'm not saying the slopes are zero, I'm just saying when the slopes are equal.

Have you found the max of that gap?

So, I need to do a little, just a little bit of house keeping here.

And I wanna say, you just watch this for a minute.

I wanna set profit is equal to total revenue minus total cost.

Now, if you were to show that function to anybody and say Calc one,

the very first calculus class, and say hey, how would you maximize profits?

>> That person in that calculus class would say,

well I know I would take the derivative of profit, with respect to output.

And I'd set that equal to zero, that's the first order condition,

that you would do when you find the maximization of a problem.

Well, the derivative of profit, with respect to quantity, is the same thing as

writing the derivative of total revenue minus total cost,

with respect to quantity.

I haven't done anything fancy there.

Which is the derivative of total revenue over output,

minus the derivative of total cost over output, as a simple distributive property.

And I wanna set this equal to zero,

that part because that's how I know I'm gonna maximize the function.

I'm gonna set this first order conditioning to equal 0, but what is this?

This term is marginal revenue.

This term is marginal cost.

And I want those two to be equal to 0.

That means the two of them have to be the same value.

Once again, this is a more formal proof using calculus.

But the fact that the way you maximize the difference between two functions is to set

their slopes equal.

Now the reason I went through this exercise is not because I'm wanting to

turn you into budding young calculus students.

It's because I want you to know that I

haven't made any other assumptions here other than just simple maximization.

And this is gonna be great for us,

because going forward we're gonna look at all sorts of different markets.

We're gonna look at markets that have lots of players.

We're gonna look at markets that have one player, we call that a monopoly.

We're gonna look at markets that have a few number of players,

that's called oligopoly, competition amongst the few.

We're gonna look at cartel markets.

We're gonna look at all sorts of markets.

And every time, all the firms in those markets wanna do this.

This is the fully general rule for profit maximization.

They go to sleep at night saying the same mantra,

marginal revenue equals marginal cost.

The intuition of this is imagine if you will that you're thinking

about your cash register at your store.

If the marginal revenue of an extra unit you sell

exceeds the marginal cost, sell it.

Cuz that marginal revenue is the extra revenue coming in, and

the marginal cost is what it costs you to make that.

If they're paying you more than what it costs to make it, do it.

It's raising the pile of coins in the cash register at the end of the day.

If it turns out the extra revenue is less than what it costs to make it,

don't be selling that unit, stop.

So, only when marginal revenue equals marginal cost are you in a happy spot, and

that's the point when you're making the most money in your front.

And we're gonna look at that over and over again as we go forward.