3. Consider an economic model with three industries: agriculture, man- ufacturing and energy. The model has Leontief input-output matrix [0.6 0.1 0.1] A = 0.2 0.4 0.2 0.1 0.4 0.2 (With the columns corresponding to the industries in the order listed). (a) If there is external demand for 800 units from agriculture, 1600 units from manufacturing and 400 from energy then calculate the total production required from each sector to meet this demand. (Note that you must show the matrix equation that you are solv- ing, but calculations can be done using technology.) (b) How many units of production are used by each of the three industries to meet this demand?

3. Consider an economic model with three industries: agriculture, man- ufacturing and energy. The model has Leontief input-output matrix [0.6 0.1 0.1] A = 0.2 0.4 0.2 0.1 0.4 0.2 (With the columns corresponding to the industries in the order listed). (a) If there is external demand for 800 units from agriculture, 1600 units from manufacturing and 400 from energy then calculate the total production required from each sector to meet this demand. (Note that you must show the matrix equation that you are solv- ing, but calculations can be done using technology.) (b) How many units of production are used by each of the three industries to meet this demand?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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d) Give three (3) reasons why you believe Contractor 2 never submitted a proposal? e) After setting the equations in matrix form from part b) above, calculate all the cofactors of Matrix A. f) Which of the three resources do you expect Contractor 1 to price the most? Give two (2) reasons for your answer. g) Hence or otherwise, determine the price of Contractor I's labour, machinery and technology.
Linear Algebra
II. Is the matrix B = [100] 1 502 3 0 € M3 (R) diagonalizable? Justify your answer.
5. Choose the following statements are True (T) or False (F): (a). det(A + B) = det (A) + det (B) (b). A system of linear equations is consistent if it has at least one solution (c). The transpose of a upper triangular matrix is a lower triangular matrix (T) or (F) (T) or (F). (T) or (F).
A simplified version of input-output analysis of a national economy has the following input-output matrix: Agriculture Manufacturing Households 0.245 0.051 0.099 0.279 0.433 0.011 A. Agriculture Manufacturing Households 0.102 0.291 0.372 units of Manufacturing are need to produce one unit of Households B. Given Demand (in billions of dollars) for the three sectors are as follows 32.6 = Manufacturing, 3.5-Agriculture 31.8-Households Find the amount of each commodity that should be produced (nearest 0.1 billion) = Agriculture - Manufacturing Households C. If the external demand of Households raises by $1 billion then manufacturing production needs to increase by $ billion (nearest 0.01) in order to meet that increase in household external demand
8. In the closed model of Leontief with food, clothing, and housing as the basic industries, suppose that the input-output matrix is A= At what ratio must the farmer, tailor, and carpenter produce in order for equilib- rium to be attained?
2. Setup: Suppose we know the following: [1 10] 1 10 X = 1 12 1 15 [114] Y = 2 = € -0.25 Var(8) = 9. 0.25 7.356 -0.587] -0.587 0.048 Identify the following (only algebra required, no complicated matrix calculations): (a) What are the x-values in the dataset? 1 (b) Find the equation of the regression line in the form ŷ = B₁ + B₁x. (c) Find Var(8o), Var (3₁). (d) Find COV (30, 31).
3. Determine the rank and nullity of the matrix 2 -1 1 -1 A = -1 -1 1 4 1 -3 -3,
f0.2 0.3 0.2] [30] (c). If input matrix is 0.4 0.1 0.2 and its final demand is 15, what are the solution lo.1 0.3 0.2l liol output levels for the three industries? (Round off answers to two decimal places.)
II. Is the matrix C = 1 1 i 2 1 € M3(C) diagonalizable? Justify your answer.