The Leontief production equation, x = Cx + d, is usually accompanied by a dual price equation, where p is a price vector whose entries list the price per unit for each sector’s output, and v is a value added vector whose entries list the value added per unit of output. (Value added includes wages, profit, depreciation, etc.) An important fact in economics is that the gross domestic product (GDP) can be expressed in two ways: Verify the second equality. [Hint: Compute pT x in two ways.]

Solution 11ETo show that , note that the price equation is given by Take transpose on both sides gives Thus , multiply both sides from the right by x gives Hence …… (1).Also the Leontief production equation is , multiply this equation by from the left side gives Hence …… (2)From (1) and (2) Hence