Assume that a and b (b is greater than a) indicate the quantity of supply on a linearly increasing supply curve. How can be the area formed by those two points under the supply curve interpreted? The interpretation should be made independent of a demand curve. That means no equilibrium price and producer surplus to account for. Could that be the difference between production costs for the given range of quantity?
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$\begingroup$ Why do you tag it as producer surplus while writing there is no producer surplus to account for? $\endgroup$– GiskardCommented Feb 6, 2017 at 11:33
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$\begingroup$ Because the calculation of the questioned region is mathematically similar to the calculation of producer surplus. The expertise for the calculation of the producer surplus can assist for the corresponding interpretation. $\endgroup$– DirkCommented Feb 6, 2017 at 11:39
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$\begingroup$ It cannot: no price is given. The only similarity is that both are areas. $\endgroup$– GiskardCommented Feb 6, 2017 at 11:41
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$\begingroup$ I don't think so. $\endgroup$– DirkCommented Feb 6, 2017 at 11:47
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Your intuition is right, but you are not accounting for fixed costs.
The supply curve is the part of the marginal cost curve above its intersection with the average variable cost curve. Marginal costs are defined as the derivative of the cost function (or the variable cost function as the derivative of fixed cost is zero).
To get the area you integrate. That is, you get back the variable cost. So the area below the supply curve between $a$ and $b$ is the difference of the variable costs.
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$\begingroup$ Thanks for your reply and for mentioning about the fixed costs. I think it can't be the variable cost. Let us assume function f(VC) that AC=f(VC)=VC.Q+FC. Average Cost (AC), Variable Cost (VC), Quantity (Q) and FC (Fixed Cost). The area of the trapezoid equals to (f(a)+f(b))/2*(b-a). I claim that this equals to the cost of supply given range of supply (b-a) $\endgroup$– DirkCommented Feb 6, 2017 at 12:15
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$\begingroup$ Not sure what you are calculating here. Total cost C(q)=VC(q)+FC, AC=C(q)/q, MC(q)= C'(q)=VC'(q). The supply curve is a part of MC. Maybe coming from the producer surplus(PS) angle. Profit = PS -FC and alternatively Profit = PQ- C= PQ- VC-FC. Now PQ is a retangle divided by the supply curve. PS is the part above the supply curve. PQ=PS+VC. $\endgroup$– BayesianCommented Feb 6, 2017 at 12:49
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$\begingroup$ A supply curve for gasoline: khanacademy.org/economics-finance-domain/microeconomics/… For example: the area between a=500 and b=550. So, the area under the corresponding region doesnt have a meaning? $\endgroup$– DirkCommented Feb 6, 2017 at 14:08
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$\begingroup$ Interpreting the supply curve as mentioned above, the meaning of this area is as described above. $\endgroup$– BayesianCommented Feb 6, 2017 at 14:40
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$\begingroup$ I see that there is a misunderstanding between long run and short equilibrium. For long run equilibrium one has to consider fixed costs. That's why your first answer is confusing and wrong interpretation. I interpret the area under the supply curve in the link as e.g. the cost of next 50 Mil. Gallons of Gasoline for increasing supply from 550 to 600 Gallons of Gasoline. $\endgroup$– DirkCommented Feb 6, 2017 at 16:08