Basically, I'm trying to understand why the total surplus is maximized at the equilibrium and what happens if the price isn't at the equilibrium.

Say the price of a good is the equilibrium price. Now make it more expensive. I know that after a while the price will adjust to the equilibrium again, but what will happen before that? I'm trying to use an example but there are things I can't fill in:

The equilibrium price of the good is \$20 and the equilibrium quantity is 20. Given a straight demand and supply curve and a maximum buyer's imposed value of \$40, the consumer surplus is $\frac{1}{2}(40-20)\cdot20=200$ and the producer surplus is $\frac{1}{2}(20-0)\cdot20=200$.

Now make the good \$30. The quantity demanded falls to 15 and the quantity supplied rises to 25. Now, the consumer's surplus is the triangle I marked in blue, $\frac{1}{2}(40-30)\cdot15=75$ (because only 15 items will be sold), but what about the producer's surplus? Is this the triangle I marked in red? I think not, because that seems to imply that the price is only \$10. But if not, what is the producer's surplus, and why?

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Thanks in advance and my apologies for the possibly confusing phrasing.

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    $\begingroup$ This question boils down to "what is producer's surplus?" which, without the homework element is a much better question in my opinion. $\endgroup$ – Giskard Apr 18 '18 at 9:38
  • $\begingroup$ Maybe you could think about who ends up with the rectangular chunk between p=10 and p=30. $\endgroup$ – Dan Apr 18 '18 at 11:12
  • $\begingroup$ @Dan I don't really know. If the price rise were due to a tax, that area would be the tax revenue, but I don't know what the area means when there is just a price change not due to taxes. $\endgroup$ – Sudera Apr 18 '18 at 11:20
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    $\begingroup$ @Sudera It seems like you're close. If the price rise were due to a tax, that chunk of money would go to the government. If it's just because the producer put the price up, where does that money go to? $\endgroup$ – Dan Apr 18 '18 at 11:26
  • $\begingroup$ @Dan Oh I guess it just goes to the producer then. Thanks for your help! $\endgroup$ – Sudera Apr 18 '18 at 11:45

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