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Economists’ Untold Secrets 040: Walras’ Puzzle I

In his element, Walras said: The buyer of a thing is the seller of that which he gives in exchange. The seller of a thing is the buyer of that which he takes in exchange. and he used an equation to simplify this statement. The buyer of A is the seller of B, which he gives in exchange. The seller of B is the buyer of A, which he takes in exchange. For example, if John buys 10 Apples each costing $2, he must sell 20 Beef each costing $1. And this equation must hold irrespective of any price. Define Pa as the relative price of A in terms of B, in the above example the relative price of A is 2 Beef per Apple. Then, Walras’ first equation can be transformed into the second one. To verify Walras’ theory, I insert some numbers into an excel worksheet for price ranging from 0 to 7. Then, I calculatethe demand for A according to 7 minus PA. For example, when pA is 0.2, Da is 6.8. Relative price of B is simply the inverse of PA. So, the inverse of 0.2 is 5. Supply of B is calculated according to the second Walras’ equation. So, 0.2 times 6.8 is 1.36. Then, I plot Da against Pa, and obtain a negative curve, which looks like a demand one. However, when I plot Ob against Pb, I obtain this curve, which does not look like a supply one. This is Walras’ puzzle: he failed to prove his own law, to derive the supply curve from a demand curve. Without a proper supply curve, there can never be any proper economic theory.

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