Analyzing Non-Linear Market Equilibrium
An economist is analyzing a market for a specialized component. The market is characterized by the following non-linear inverse functions, where P is the price in dollars and Q is the quantity in thousands of units:
- Inverse Demand: P = -Q² + 2Q + 90
- Inverse Supply: P = Q² + 8Q + 10
By setting the two functions equal to each other, a quadratic equation is formed that yields two mathematical solutions for the quantity Q. Your task is to find the single, economically valid market equilibrium. Calculate both potential quantities, determine the correct equilibrium quantity and price, and explain the reasoning for discarding the extraneous solution.
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