(Solution) - The demand for air polluting backhoes in Peoria is PD -(2025 Original AI-Free Solution)

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The demand for air-polluting backhoes in Peoria is PD = 48 - Q. The air pollution creates a marginal external cost according to MEC = 2 + Q. Supply of backhoes is given by PS = 10 + cQ. If the socially efficient level of backhoes is Q* = 12, find the tax that induces the socially efficient level of backhoes in equilibrium and the value of c.