4-1.1. Firm Optimization Behavior

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From the course by University of Illinois at Urbana-Champaign

Firm Level Economics: Consumer and Producer Behavior

416 оценки

University of Illinois at Urbana-Champaign

Firm Level Economics: Consumer and Producer Behavior

416 оценки

Course 1 of 7 in the Specialization Managerial Economics and Business Analysis

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.

From the lesson

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.

4-1.1. Firm Optimization Behavior7:57

4-1.2. Maximizing Profit7:30

4-1.3 Maximizing Profit Graphically6:30

Meet the Instructors

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

[SOUND] We're working with the firm and

we're trying to figure out how

the firm maximizes profits.

We've now taken a great deal of time to construct cost curves.

And we have to think about how the firm is gonna take these cost curves, and

work with them to optimize.

And so, in this particular module, we're thinking about how firms optimize.

Our goal is gonna be to understand individual firm behavior.

The firm wants to maximize profits, we know that.

So for this lesson we're gonna say the firm knows the following.

One, its own set of

cost curves associated with production.

And two, it also knows an exogenously given price, and we'll call that P sub 0.

So, right now, the main goal for

the course is to think about, figuring out price.

But right now, we're stepping along the way and

we wanna think of how a firm will optimize for any given price.

And once we know that, then we'll start to sort of move price around and

see how they respond.

Way back in the very first lesson,

we looked at how firms output [INAUDIBLE] and I mean firms in the grand total.

Market output changed as prices were changed,

raising prices caused firms to put forth more output, lowering caused forms to put

forth lower levels of output across the entire market, that was our supply curve.

Well, today we wanna start a lesson where we're thinking about pushing

forward on how that one individual firm will optimize for one particular price.

Let's just pick a price out of thin air, and

work out the optimization profit, okay.

Great, so the firm wants to maximize it's own profit,

so firm i will maximize the profit.

So I'll denote that profit is profit of one individual firm, firm i.

Now the profit for firm i is equal to total revenue minus total cost.

If we could draw a graph for total revenue and

draw a graph for total cost, we could do that.

We could figure the output level for that particular firm that would maximize

profits, by just taking the difference between those two curves.

Well let's start with total revenue.

Total revenue's pretty easy.

Total revenue is just price times quantity,

in this case price is given parametrically, times quantity.

Price for this lesson is some fixed price and

we're spending the whole lesson thinking about how the firm will make its decision

of production based on what that fixed price is, understanding its cost curves.

What's that total revenue function looks like?

It's not too difficult.

It looks like this, it's a straight line.

How do we know it's a straight line?

Well the definition of a straight line,

it's a graphical construction that has constant slope.

A linear function has a constant slope, that's what this is.

What is that constant slope, well that constant slope is just this.

I have exogenously given this price, suppose it's $3 a unit.

$3 per jar of mayonnaise.

No matter how many jars of mayonnaise you produce, you're gonna get $3 for each one.

That means that along this line, the total revenue function will be a straight line.

Marginal revenue is defined as the slope of a total revenue function,

which is just basically the change in total revenue for the change in output.

And the slope then,

which would be the marginal revenue, is equal P sub 0 in this case.

We know that cuz that's the constant slope along that straight line.

Okay, so to maximize profits, we need to take this type of curve and

add our cost function.

We know what that looks like, cuz we built those before.

So let's draw another graph.

We know that our total cost is a fixed cost component,

plus a variable cost component, which gives us total cost that looks like this.

Now, my total revenue, price times quantity.

Price is parametric.

Price is given exogenously.

Okay, so it's a fixed number.

It means it's a straight line which I'm going to draw for the total revenue, and

it looks something like this.

So my total cost curve and

my total revenue curve look like this and how do I maximize profit?

I wanna maximize profit, which

is the same thing as saying maximize the difference between revenue minus cost.

On this picture, that looks like it's about right here.

So we'll say that at this particular output point,

this vertical gap is maximized.

And so we'll label this point as q*.

Given what the firm knows about its costs, we've spent the last lesson

slogging it through figuring out what these cost curves look like and

how they come from the production function in the first place.

We know what costs look like.

And given that the firm is faced with an exogenously given price,

this would be the output level that maximizes profits for the firm.

Now there's probably a better way to think about this.

And so what I wanna do is, before I switch from this page, just so

that you understand we'll call this point alpha and we'll call this point beta.

Profit at q* is equal to alpha minus beta.

That vertical gap is the profit.

It's probably a little more satisfying instead of just eyeballing it,

why don't we build a profit function?

Why don't we build a profit function on this graph, and

in fact it's pretty easy to do that.

If we looked at that picture again and I asked you to build a profit function,

the easiest way to do this is think about the zero points to begin with.

We know that at this particular output point, what's profit?

Zero.

When revenue, at this particular output point,

total cost is exactly the total revenue, profits are zero.

At this particular output point we know profits are equal to zero.

Now for outputs between these two, interior to this range what are profits?

Well they're positive.

Revenue is everywhere above cost in those.

Outputs to the right of this point, costs exceed revenue.

Outputs to the left of this point, costs exceed revenue.

So now that we know our zero points, let's draw this graph.

And the graph would have positive segment here and

to the left of this point, it's gonna be negative.

And to the right of this point, it's gonna be negative.

In fact it's gonna scream down negative as you can up here on this graph.

Total cost curve is really arching up quite rapidly because we're

at that point where marginal returns has really set in.

What's it look like down here at the end?

Well, you know, in fact, it's gonna go down here and

then it's gonna fix to go back up and then it's gonna end about right here.

We know this is equal to minus fixed costs because we know that if the firm produces

zero, it has zero revenue, it has zero variable costs, but even if it's producing

zero, it still has to pay it's fixed costs because we're in the short run.

The short run can't get out from underneath that.

You've got that brick and

mortar you've gotta pay for, even if you're producing zero of your output.

And that means we could find our profit maximizing point by finding the peak of

this hill.

Right at the peak would be q*.

It's the same thing as eyeballing, only now a little bit more systematic,

by putting this in terms of a graph.

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