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Sources: p 289, Principles of Microeconomics (7 Ed, 2014) by N G Mankiw
p 259, Modern Principles of Economics (2 ed, 2011) by Tyler Cowen, Alex Tabarrok

Definitions: Profit $:=$ Total Revenue $−$ Total Cost = TR $−$ TC

Total Revenue $:=$ Price $\times$ Quantity and Average Cost = $\dfrac{Total \, Cost}{Quantity}$

$\Rightarrow ... \Rightarrow$ $\color{darkred}{\text{ Profit = (Price $-$ Average Cost) $\times$ Quantity }}$

Please help me dig deeper than the maths, which I already understand and so ask NOT about. Accordingly, I ellipted the mathematical proof with the ellipsis above.

What's the intuition behind the last (reddened) equation for profit? I ask only for intuition; please omit any formal arguments or math proofs.

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    $\begingroup$ This is the usual definition of profit (i.e. the excess of revenues over costs). Please help us understand what kind of "intuition" are you seeking. I honestly fail to see what is unclear in the fact that if I sell each unit for 10 and each unit has cost me on average 8, I earn an average profit of 2 per unit, and so my total profit will be 2 times the number of units sold? $\endgroup$ – Alecos Papadopoulos Jun 3 '15 at 0:59
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The intuition is simple: Profit can be represented as the profit per unit output, which is the discrepancy between what the firm receives for selling the unit (the price) and the average cost of producing that unit at the given level of output (ATC), multiplied with the number of units of output (taking you from profit per unit to total profit).

Example: You produce widgets at a constant marginal cost of \$1 per widget. You find it optimal to sell 10 widgets on the international widget market, where you can fetch \$1.05 per widget. You profit is the profit per unit of \$.05 times the 10 units you sold, summing to a total of \$0.50.

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  • $\begingroup$ note that this vision is very artificial, so I don't think there is any better answer than "the maths" in this case: multiplying average cost by quantity is a bit of an artificial step, that is done only in order to compare cost with price in a global context. $\endgroup$ – VicAche May 26 '15 at 10:33
  • $\begingroup$ @VicAche I wouldn't necessarily describe it as "artificial", rather since it's just manipulating an accounting identity, there really isn't much "depth" to be grasped in the first place I guess? $\endgroup$ – Hessian May 26 '15 at 13:48
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    $\begingroup$ what I wanted to say is that, there is no fundamental intuition to be found from dividing then multipling a given quantity. "artificial" may have been an overstatement :) $\endgroup$ – VicAche May 26 '15 at 14:18

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