(20 marks) A Home rm has high- and low-skilled workers that it can move freely between two activities: manufacturing (n) and marketing (r). The workers, if fully employed, create a production possibilities frontier (PPF) for the Home rm of n2 + r2 = 5000 , where manufacturing is measured on the horizontal axis and marketing is measured on the vertical axis. The slope of the PPF at any point is given by E. The Home firm uses those two activities to produce a nal good, y, given by r the production function y = nr. The slope of the Home rm's isoquants is given by 1 , again where :7 manufacturing is measured on the horizontal axis and marketing is measured on the vertical axis. Start from a state of autarky. a. (2 marks) Calculate the optimal quantities of manufacturing and marketing that the Home rm will use in autarky. (Hint: think, on the diagram, where the optimal quantities occur in autarky and how they relate to the PPF and the isoquant.) b. (2 marks) Calculate the amount of output the Home rm can produce in autarky