Consider the market for a specific fruit product (GrapplesTM) where the demand is given by: Q QD = 10, 000-400P The inverse supply (i.e. "Private Marginal Cost") is: PMC = 5 + 0.0075Q 1 The production of Grapples uses large amounts of fertilizer which results in runoff and damage to the water in adjacent rivers and streams. The marginal cost of this pollution is given by the Marginal External Cost equation: MEC = 0.0025Q Grapple producers are not liable for these harms and so ignore them in their production decisions. (a) Find the competitive equilibrium price and quantity. (b) What is the efficient quantity of output? (c) Calculate the deadweight loss created by the externality. (d) Suppose the government imposes a tax (per Grapple). What tax amount will result in the efficient quantity of Grapples? (e) Calculate the following: Before the tax: CS, PS, and the total external cost. After the tax: CS, PS, government tax revenues, and the total external cost. Show that the deadweight loss is the difference between the welfare with the tax compared to without the tax