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A factory and an amusement park are both located next to a residential neighborhood, creating a noise problem that the local government is considering regulating

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A factory and an amusement park are both located next to a residential neighborhood, creating a noise problem that the local government is considering regulating. The amusement park's total cost function for reducing the noise level by D decibels is TCa=(4/3)D2TCa=(4/3)D2. The factory's total cost function for noise reduction is TCf=4D2TCf=4D2. The social marginal benefit of noise reduction is SMB=40−2DSMB=40−2D .

What is the socially optimal level D∗D∗ of total noise reduction? Find the amount of noise reduction done by the factory (D∗fDf∗) and by the amusement park (D∗aDa∗) at the optimal outcome.