Biology Forums - Study Force

The city of Econoville currently does not charge a fee to residents to use the city garbage services.  The marginal social cost of garbage is: MSCd (gd) = 23gd, where gd is tons of garbage disposed per year.  The marginal benefit function of garbage removed from residences is: MB(g) = 1,000 - 2g.   Given the lack of a payment plan for garbage disposal, what level of garbage are the city residents disposing each year?  Is this level of disposal efficient?  Why or why not?  Suppose the marginal cost of recycling is: MSCr(gr) = 46 gr.  The marginal benefit of garbage removed from residences is: MB(gd, gr) = 1,000 - 2(gd + gr).  What is the optimal level of garbage disposed and garbage recycled in Econoville?

With the payment plan, residents set: MB(gd) = 0  1,000 - 2 gd = 0  gd = 500.  The marginal social cost of this level of garbage disposal is $11,500.  This level of disposal is not efficient because the marginal benefit is zero while the marginal cost society pays is $11,500.  The efficient level of disposal sets: MB(gd) = MSCd(gd) = 1,000 - 2 gd = 23 gd  gd = 40.  With recycling as an option, the optimal levels require: MB(gd, gr) =  MSCd (gd) =  MSCr(gr).  Equal marginal social costs of disposal and recycling require: 23 gd = 46 gr  gd = 2 gr.  This implies:
MB(gd = 2 gr, gr) = 1,000 - 2(3 gr) = 46gr  gr = 19.23.  Thus, optimal garbage disposal is 38.46 units.