Problem 6. The economy of a country is divided into four sectors which have the following productivity characterizations. The production of 1 unit of output of (1) petroleum requires 0.2 units of transportation, 0.4 units of chemicals, and 0.1 unit of itself (2) textiles requires 0.4 units of petroleum, 0.1 unit of textiles, 0.15 units of transportation, and 0.3 units of chemicals (3) transportation requires 0.6 units of petroleum, 0.1 unit of itself, and 0.25 units of chemicals (4) chemicals requires 0.2 units of petroleum, 0.1 unit of textiles, 0.3 units of transportation, and 0.2 units of itself (a) Construct the technology matrix. (b) Construct the Leontief matrix for this problem. (c) If the economy produces 900 million dollars of petroleum, 300 million dollars of textiles, 850 million dollars of transportation, and 900 million dollars of chemicals, how much of this production is internally consumed by the economy? How much is produced for the external demand? (d) Find the inverse to Leontief matrix of the problem (calculators are allowed in this part of the question). Explain the economical meaning of the columns of the inverse matrix. (e) Given the economy productions in (c) suppose that the demand in textile decreased 10% whereas other external demands remained unchanged. Find how this change in demand of textile affected other sectors of economics in percents (calculators may be used in this part of the problem).