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Differential Equations in Economics
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In a simple economic model, the demand for a product is given by the differential equation (\frac{dQ}{dt} = -aQ + bP), where (Q) is the quantity demanded, (P) is the price, (a) and (b) are positive constants. What is the equilibrium price?
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A
$\frac{b}{a}$
💡 Explanation:
The equilibrium price is the price at which the quantity demanded equals the quantity supplied. In this case, the quantity supplied is constant, so the equilibrium price is the price that makes the quantity demanded equal to the constant quantity supplied.