MR=MC - Why?

March 21, 2007 9:07 AM

EconomicsFilter: why does profit maximize when marginal revenue = marginal cost?

To get this out of the way: no, this is not for any sort of assignment, research paper, etc.

As a student of economics, I've always been told that in perfect competition, MR=MC. But one thing I've been struggling with lately is - why?

I understand why MC > MR would be bad, since it would cost more to produce an additional unit than that same unit would generate in revenue. But what I don't understand why MR > MC would continue until MR = MC. Wouldn't one want its marginal revenue to be greater than its marginal costs? I mean, if profit is maximized when there is the greatest difference between total revenue and total cost, why is the same not the case here? Let's say if MC = $10 and MR = $20, why wouldn't a producer just call it a day and be happy with a $10 marginal profit (please correct me if this example is flawed).

I've looked at some textbooks for their explanation but it really didn't answer my question. Furthermore, I haven't had too much luck online, and Wikipedia's or Wikibooks' explanation isn't too satisfactory either. Perhaps the Hive Mind has a good explanation...

posted by champthom to work & money (10 comments total)

My armchair-economics understanding is this: so long as MR > MC, there is money to be made off of further production. Stopping short of that equality is a failure to maximize the total profit you'd get from producing right up to the asymptote.

So you ask why a producer wouldn't just call it a day. The answer is, they might just, but it'd be a choice to favor limited production with a good per-unit profits vs greater production with lower per-unit profits but greater total profits. Making $x-per-unit for n units isn't, in theory, a rational alternative to making $y > $x*n on more-than-n units of production.

But what's rational in microeconomic theory and what's appealing to an actual person may differ, so you might see people willfully violate that precept in practice. 'Rational' is in econ as in game theory a tricky term.
posted by cortex at 9:23 AM on March 21, 2007

Say you're producing at below optimal output. Here, MR is greater than MC (say MR = $20 and MC = $10 as in your example).

Now, produce one more unit. Say MR now falls to $19 and MC rises to $11. You've just made $8 more profit than you were making before. Produce another, and you make $6 more profit again.

This continues until MR is equal to MC, at which point you are maximising profit, and hence "marginal profit" is zero.

Wouldn't one want its marginal revenue to be greater than its marginal costs?

No, absolutely not. What does "marginal" mean? It means the cost or revenue of producing one more unit*.

If MR is greater than MC, that means the business could increase total profit by MR-MC by producing an extra unit. It should continue increasing production until MR=MC, which is where total profit is maximised.

* Okay, technically it's to do with derivatives, but the "one more unit" definition is good enough.
posted by Aloysius Bear at 9:26 AM on March 21, 2007

But what I don't understand why MR > MC would continue until MR = MC. Wouldn't one want its marginal revenue to be greater than its marginal costs?

At one level, this is just dealing with an edge condition. For a real good, the odds that MC would ever rise to *exactly* equal MR are essentially zero -- with granular goods, you'd expect one item to have MR greater than MC and the next to have MR less than MC, so the firm should not produce that last item. In real life, a firm will be operating under a best-guess approximation of MC in any case, which would further make the edge-case even more irrelevant.

I mean, if profit is maximized when there is the greatest difference between total revenue and total cost, why is the same not the case here?

MC=MR is the pint that maximizes profit. Profit is an area, not a line.

Think of a figure with MR and MC. Profit is the area above MC and below MR. This area is maximized when the firm produces until MR=MC.

Say you're producing at below optimal output. Here, MR is greater than MC (say MR = $20 and MC = $10 as in your example).

Now, produce one more unit. Say MR now falls to $19 and MC rises to $11.

It's usually simpler to just think about constant MR = market price.
posted by ROU_Xenophobe at 9:41 AM on March 21, 2007

Yes, in perfect competition MR will be constant, and equal to average revenue and price. But profit-maximisation by equating MC to MR isn't specific to perfect competition, it's more general than that.
posted by Aloysius Bear at 10:08 AM on March 21, 2007

Yeah, but it's just easier to think about MR being constant while the MC cost curve shifts around. That way there's only one real variable, the MC.
posted by ROU_Xenophobe at 10:56 AM on March 21, 2007

Essentially, (insofar as econ class has taught me) Cortex has it.

The thing about perfect competition is that there are supposed to be no barriers to entry or exit. So let's say Firm A decides to up the price of widgets a little, in order to make more of a profit. Thus, they are setting P = MR > MC. This is what a monopolist does, and, indeed, monopolists can make extra profit by doing this.

But because of perfect competition, as soon as Firm A does that, some guy will come along and say, "Hey, I can undercut Firm A's price!" So they make some widgets and sell them for some other price P' < p. since they're making the same stuff and selling it for less, this will lower the price to p', and firm a will have to keep up by setting their price for p'.

It is clear that as long as the market price is greater than the marginal cost, some guy can always come along and undercut the price. So as long as firms can do this without facing large costs of entry, MR will equal MC.

Aloysius Bear --- your logic assumes that the producer has the power of price discrimination. We generally think that, instead, a producer must sell all units at the same price. This means that a monopolist will not make optimal profits by setting P = MC. Say you're making K units, and you want to make a K+1st. If MR for the Kth unit was 20, and MR for the K+1th was 19, then you have to sell all K+1 units for 19. If you sell them for 20, then nobody will buy the K+1st unit (since MR is smaller than 20). So what the producer would like is for the price to equal the average cost.
posted by goingonit at 11:49 AM on March 21, 2007

Sorry; rather, a monopolist producer would like to price the good so as to achieve the point of minimal average cost, thus resulting in MR > MC. But in perfect competition, because of free entry, the producer doesn't get to set the price.
posted by goingonit at 11:58 AM on March 21, 2007

A quick definition: Marginal Profit = Marginal Revenue - Marginal Cost. It also means thethe additional profit made by making one more unit of product

Let's say I make ten widgets right now and make $10 dollars in profit. My marginal profit is $3. (MR-MC). So I decide to make one more widget (number 11). My total profit is now $13 ($10 + $3).

Now My MP Readjusts to $2 (for example), since it's still positive I make number 12, my total profit is now $15 ($13 + $2).

Let's say at unit 13 that my MP is 0$. I could make widget number 13 and not lose any money, but I wouldn't make anymore profit either. Either way lets say I make widget 13 just to appease a good customer, my total profit is still $15 (my revenue is greater but my costs are the same amount greater).

Now to make widget 14, my marginal profit is -1, Marginal Costs have exceeded Marginal Revenue. At this point to make widget 14. Now I lose $1 of total profit. At this point my total profit is $14. I've sold more units but costs have gotten so high that I'm losing money.

So while I'm making a profit at unit 10. I make more profit if I sell unit 12.

At least this is the rough method that I understand it and I had a really bad econ prof.
posted by bitdamaged at 12:04 PM on March 21, 2007

I was also wrong about Aloysius Bear being wrong. It's a good thing I'm not still taking microeconomics anymore...
posted by goingonit at 12:10 PM on March 21, 2007

goingonit: your logic assumes that the producer has the power of price discrimination

Which bit of my comments implied that? I may have made a slipup somewhere, but I was trying to explain in as generalised way as possible how MC=MR maximises profit.

You're right that P=MC in perfect competition, and P>MC in an monopoly. But you seem to be mixing up the details of perfect competition with the reason why MC=MR maximises profit. The questioner asked two different questions: why is profit maximised at MC=MR, and why does MC=MR for all firms in perfect competition.

a monopolist producer would like to price the good so as to achieve the point of minimal average cost, thus resulting in MR > MC

No, every firm wishes to maximise profit. Profit maximisation is, by definition, where MC=MR.

The monopolist will price at MC=MR, but since MR≠P it will not produce at P=MC.
posted by Aloysius Bear at 12:13 PM on March 21, 2007