Solve clearly

Sylvania is a small economy producing two products, X and Y, using two factors of production, capital and labour, under constant returns to scale. Capital and labour are freely mobile between sectors, but immobile internationally. Let Q x and Qy be the output quantities. Consumers have a utility function U(Dx, DY) = Dx + 2Dy, where Dx and Dy are consumptions of X and Y. The price ratio is defined as P= Sylvania's production possibility frontier (PPF) is defined by the equation Qx + 6QY = 15, which has slope given by the marginal rate of transformation MRT = - d day _ 12x dQ x 6 QY Answer the following questions. All numerical answers must be expressed as decimals (not whole numbers or fractions) and be accurate to two decimal places. (a) Calculate Sylvania's autarky product price ratio P = P (b) Calculate Sylvania's autarky production quantity for X: (c) If the world price ratio is P = 1, calculate Sylvania's production quantity for X under free trade: (d) If the world price ratio is P = 1, calculate Sylvania's income expressed in units of product X under free trade: (e) Suppose that the production function for product X is given by F(Lx, Kx) = LY Ky , where Lx, Kx denote the input quantities. If Sylvania's factor price ratio (wage-rental ratio) is w = = = 2, calculate the capital-labour ratio used in the production of good X