March 24 - Monopolies - Day 2 - Graphs and More

Let's start by looking at the answers for the chart posted in yesterday's blog.

Price	Quantity	Total Revenue (TR)	Average Revenue (AR)	Marginal Revenue (MR)
$100	1	100	100	100
$90	2	180	90	80
$80	3	240	80	60
$70	4	280	70	40
$60	5	300	60	20
$50	6	300	50	0
$40	7	280	40	-20

If you don't understand something on this chart, please ask!


Yesterday we discussed why in a monopoly Marginal Revenue (MR) is always less that Price (P) and Average Revenue (AR).

What about Total Revenue (TR)?  How is that different in a monopoly?

In a PC firm TR is a straight line that goes diagonally upward.  This is because you can always sell another unit for the same price.  Thus as quantity increases TR always increases by the same amount, the price.

In a Monopoly things are different.  Since P and AR go down as quantity increases, it means TR does not go up by the same amount every time.  In fact, it will eventually start going down.

We can see all of this on the chart that is above.  Note how the amount TR increases (also known as MR) slowly gets smaller and smaller.  Then once the MR becomes a negative number TR starts going down.

Now for some graphing!!!!!!!

Let's start with the Total Cost Graph (TCG).  Because TR goes up and then comes back down, it is shown by an arch or parabola.  The TC and TVC lines on the TCG are still the same.  Here's a sample graph:

Even though we now have an arch instead of a diagonal line, the rules for our TCG are essentially the same.  Since Profit is Revenue minus Cost, then Total Profit is Total Revenue minus Total Cost.

Tπ = TR - TC

If the TR line goes above the TC line at any point, then just like in a PC graph we are looking for the place where the TR line is vertically the highest above the TC line.  It the TR does not go above the TC line then we are losing money and are looking to minimize our losses.  To do that we look for the place where the TR line is vertically the closest to the TC line. 

Now for the Marginal Average Cost Graph (MACG).

All of our cost lines on the MACG are going to look the same.  Our DARP line is now downward sloping and our MR line slopes down faster below it.   (The MR and DARP lines are NOT parallel.  They will always look like a pair of chopsticks.)

Here's a sample:

The DARP line is the line we look to for most of our data.  At any given quantity it will tell us all of our revenue and profit.  Thus, it is the line we look to when we want to determine if we can make a profit.

However this doesn't mean that the MR line is unimportant, because we know that profit is maximized at MR = MC. 

Thus, when we are looking at the MACG, the first thing we should find is the spot where the MR and MC lines cross.  If we head straight down from there, that will tell us our profit maximizing quantity.

Once we have found that, we are pretty much done with the MR line.  However we still need to determine the price.

Fortunately we have a Price line.  (After all it is the P in DARP).

At the quantity we determined, we go straight up until we hit the DARP line.  From that point we go straight left to the y-axis.  That tells us the price we are selling at.

Monopolies and the Shut Down Rule:

Once we know how to find price and quantity, it's pretty simple to use the same logic as with a PC firm to determine whether we should shut down or not in the short term.

We still have the same four positions and we still apply the same reasoning.  We are just doing it with the DARP line (instead of a MRDARP line).  The relative height of the MR line does not impact our decision.  We only look at the DARP line.

Our four positions are:

1) Making a profit:   If the DARP line is above the ATC line at any point, then the company is making a profit in that area.

2) Breaking even: If the DARP line touches the ARC but does not go over it, then the company is breaking even.  Because DARP is downward sloping, this will be more on the side of the ATC and will NOT be at the bottom of the ATC.

3) Losing money but stay open: If the DARP line is above AVC but does not touch the ATC in any location, we are losing money but should still stay open.  The reasoning is the same as a PC firm, we are losing money, but we are covering all of our variable costs and part of our fixed costs.  We would lose more money shutting down because then we would lose all of our fixed costs.

4) Losing money and should shut down:  If the DARP Line never even touches the AVC then the firm should shut down in the short term.  If they stay open they will be losing all of their fixed costs and part of their variable costs.  Whereas if they shut down they will only owe their fixed costs.  (Because their variable cost will be $0).

Maximizing Revenue:

Last but not least we can look once again at maximizing revenue.

Remember in a PC firm revenue was never maximized.  This was seen on the MACG because the MRDARP line was perfectly elastic (horizontal).   MR was always the same.  Thus we could always sell one more unit at the market price and revenue will go up by the same amount (the price).  On the TCG we could see it because the TR line went diagonally upward forever at a constant slope.

Things are once again different for the monopoly firm.  Because the MR is downward sloping, at some point it will become zero.  Thus at some point the amount of revenue being added will become zero and thereafter be negative.  So we can find a place where revenue is maximized.  For a monopoly TR is maximized where MR is equal to zero.  It's the place where MR hits the x-axis.   On a TCG, TR is clearly maximized at the top of the arch.

Remember, even though we know where revenue is maximized, that doesn't mean that is where we are producing.  A business is not in business to maximize revenue.  It is in business to maximize profit!

That brings us to the end of the Monopoly Day 1 notes.

You should be able to complete most of the four worksheets that I gave out before we left.

Here is a list of them:

Revenue Functions of a Monopoly (Activity 3-10)
Profit Maximization by a Monopoly (Activity 3-11)
Comparing Perfect Competition and Monopoly (Activity 3-15)
PC vs Monopoly Graphs

Again I don't have the right to post the first three, but I did some poking around yesterday and I believe you can find them on the internet if you look.

Please try and complete the PC vs Monopoly Graphs sheet.  If you do, feel free to take a picture or scan it and send it to me.  I'll be glad to see how you did and help you fix any mistakes.

Tomorrow we'll move into the left over bits with monopolies