Derive the conditions for a Pareto Optimum in an economy in which there is only one person with utility function U(x,y) and two industries with production functions = ($ ) and =(% ) where the total amount of land in the economy is L where = $ % . Show your work. Assume all functions have the standard properties. (5) 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 = ($ ) . That is, each unit of y produced causes external damages in the form of fewer units of x being produced. Show that the condition for a Pareto Optimum becomes = 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