4. In the same economy as in question 3, assume that the production of y causes an external cost to the x industry. Specifically, assume now that x = f(x)ay. That is, each unit of y produced causes external damages in the form of a fewer units of x being produced. Show that the condition for a Pareto Optimum becomes MRS = MRT + a where MRS is the marginal rate of substitution between x and y and MRT is the marginal rate of transformation between x and y. Finally, provide an intuitive explanation of this new condition. (5)