Why is profit maximized when MC=MR?

A question from Yahoo! Answers:

Why is a firm profit-maximising when MR=MC and not when MR>=MC?
My economics teacher has been repeatedly teaching us that the profit maximising point for firms is when marginal revenues equal marginal costs. Well, to maximise profit, wouldn’t the firm want MR to exceed MC, thus making an abnormal profit on each marginal unit?

There must be more to this than my understanding, unless my teacher is plain wrong…

OK, here is a (hopefully, comprehensible) graphical explanation:

After the company breaks even, TR usually increases faster than TC, so TR and TC begin to diverge. As q continues to increase, TC’s growth will pick up due to diminishing returns, while TR’s growth will start slowing down due to effects of diminishing marginal utility. So at some value of q (marked by the dashed line on the graph above), TR and TC will stop diverging and start converging. At that value, two things will happen:

  1. The two lines will be separated by the greatest vertical distance (after all, they just stopped diverging and they are about to start converging).
  2. The slopes of the two lines will be equal (while they were diverging, the slope of TR was greater than the slope of TC; as they start to converge, the slope of TC will become greater than the slope of TR)

Now, let’s recall that in economics, the vertical distance between TR and TC is called profit, the slope of TR is called MR, and the slope of TC is called MC. Make proper substitutions to the two statements above, and you will find that the profit is indeed maximized when MC=MR…

22 thoughts on “Why is profit maximized when MC=MR?

  1. joanne3

    wow that really cleared it up in a graphical manner (the part where the slopes of TC and TR is MC and MR, and since the slopes are equal, MC is MR)! lol thanks!

  2. brandon

    don’t know if you still see this, but it’s almost 2011 and your post just helped me out for my university class. thanks

  3. frank

    I THINK THE TR CURVE FALLS BECAUSE OF THE LAW OF DIMINISHING MARGINAL RETURNS AND NOT DIMINISHING MARGINAL UTILITY

  4. NC Post author

    Frank,

    Just think it through… Diminishing returns occur in production, so they have to affect costs (and they do; this is why MC starts sloping up after a while). Diminishing marginal utility, meanwhile, occurs in consumption, so it has to impact “the ability and the willingness to enter the market”, or, in other words, demand.

  5. A Happy Person

    Hi, I came accross your response from Yahoo Answers! and I found this incredibly helpful!

  6. Rishi

    Isn’t it much easier to draw a MC/MR curve….this will be a lot easier and much more clear…….just like “me” said !!

  7. NC Post author

    Rishi,

    Maybe, but maybe not. If you understand the derivation of MR and MC, then yes. But what if the whole concept of a derivative eludes you? That’s been known to happen…

  8. Jake

    Thanks Boss, great explanation but this is still playing on my mind; how are the slopes equal at the dashed line?

  9. joey

    The “Inquirer’s” assumption that has him confused about the issue is this:
    Not all of the Item’s produced had a MR=MC. JUST the last “Q” had that equality.

    Say for instance that Q=10 at MR=MC. AT that point, no profit is made on the TENTH Q, but the previous 9 Q’s had money made on them at their corresponding MC .

    So to understand it the way the original question was asked, you must understand that each of the previous Q’s building up to the last one WERE profitable, only the last Q was not.

  10. joey

    Pardon, I should have said that his assumption was that ALL Q’s in production Cost the same as the last Q. To correct his assumption: Not ALL Q’s in production had the same MC as the last Q, where MC=MR.

  11. ryan

    explains exactly what I was wondering (2nd year econ), Ive been rote memorising this the whole time!

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