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If demand for a product is elastic( consider the case when the price is low ), lowering the price further increases total revenue.

However, as per the law of supply, low prices cause suppliers to supply less of this elastic demand product. There will be a shortage and price must increase back to equilibrium price.

Doesn't the law of supply invalidate "total revenue rises with price drops on goods with elastic demand"?

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There is no contradiction.

The law of supply simply indicates a supply curve is upward sloping. There is no prohibition against the curve itself moving so that it intersects demand in another location, so long as the slope remains positive.

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