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Minimum profit output

R

Rupel

Member
Hey, it would be very helpful if someone could please explain how point Q1 in the attached image is the minimum profit output. Thank you.
 

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Profit = TR - TC

We can find maxima/minima by differentiating profit with respect to output and setting this equal to zero (and if we differentiate totals, we get marginals), so:

d(Profit)/d(output) = MR - MC = 0

So you get maxima/minima where MR = MC.

Then you can see from the diagram that if you are at Q1 and you increase output, because MR > MC, your revenue will increase by more than your cost, so profit increases. So Q1 must be a minimum point.

Alternatively, just imagine sitting at point Q1 and thinking about what happens if you increase / decrease output:
- if you increase output (as described above), profit increases
- if you decrease output, because MC > MR, your costs will fall by more than your revenues, so (again) profit increases.

So Q1 must be a minimum profit output level.
 
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