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Why is it that demand and supply curves are typically shown in graphs, including in Econ 101, as concave up (i.e., convex)?

I know what it entails mathematically—that if $p(q_d)$ is a demand curve, $p''(q_d)$ is positive, and if $p(q_s)$ is a supply curve, $p''(q_s)$ is positive, but what’s the intuition for why that’s usually the case?

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    $\begingroup$ They needn't be. Those are just arbitrarily drawn curves. They are just as often straight lines. $\endgroup$ – Kenny LJ Jan 4 at 4:11
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This is so because usually the marginal costs of firms are increasing in production and many economists think also at increasing rate.

Intuitively you are only willing to provide good Q if the marginal costs are less or equal to price $MC \leq P$. Providing goods to the market at price below marginal cost is irrational and hence inconsistent with basic assumptions behind supply and demand.

The reason why marginal costs are thought of as usually increasing is that the more you use up some factor of production let’s say capital the scarcer it becomes and hence the return to capital increases and hence the MC increases. Moreover, many economists believe that they also do this at increasing rate (That is if you increase the consumption of labor twice the labor costs will increase more than twice) and hence you get convexity. But this being said you can find concave cost functions and also linear cost functions as well which are neither convex or concave in many textbooks as well.

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  • $\begingroup$ Increasing MC doesn’t explain why supply is concave up—it only explains the upward slope of the supply curve. Because supply isn’t a total cost curve, it’s a marginal cost curve. So a concave up supply curve means the third derivative of the cost function must be positive, not the second derivative. $\endgroup$ – Tejas Subramaniam Jan 5 at 7:14
  • $\begingroup$ So the question is whether the marginal cost function is concave up, not whether the cost curve is concave up. $\endgroup$ – Tejas Subramaniam Jan 5 at 7:15
  • $\begingroup$ @TejasSubramaniam but as I said in my answer 1. Marginal cost is increasing 2. It is though of increasing at increasing rate (second half of paragraph 3). So it depends on a second derivative of marginal cost (or third derivative of total costs but since convexity is determined by examining second derivative I think it’s best of thinking of it as 2nd derivative of MC than 3derivative of TC). Also, supply is derived from MC of individual firms. It’s valid to just look at supply itself and just examine second derivative of supply but for intuition you have to go back to marginal cost $\endgroup$ – 1muflon1 Jan 5 at 11:43

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