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How do the role of relative prices affect how resources are allocated? And as a result, how does this effect living standards?

Would it be something along the lines of how changes of relative prices affect "what and how much" to produce, "how" goods are produced and "whom" to produce for?

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    $\begingroup$ In an ideal, competitive market, prices serve as a conduit for information, signaling producers what to producers and consumers what to consume. By the way, what's your mathematical level of sophistication? Comfortable with vectors? Solving a convex, constrained optimization problem via the method of Lagrange multipliers? Many economists have written about how prices work in colloquial language but you can also see how they convey information in a mathematical model such as Arrow-Debreu. $\endgroup$ – Matthew Gunn Aug 1 '17 at 14:42