8. In the closed model of Leontief with food, clothing, and housing as the basicindustries, suppose that the input-output matrix isA=At what ratio must the farmer, tailor, and carpenter produce in order for equilib-rium to be attained?

Given: Here is the given input-output matrix, A=4161241651618516131414 To find: The ratio must the…

Answered: In the closed model of Leontief with…

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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If A is a matrix in RmXn with {}} -5 C(A) = span %3D -2 what is m?
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
3. Determine the rank and nullity of the matrix 2 -1 1 -1 A = -1 -1 1 4 1 -3 -3,
Assume that an economy is based on two industrial sectors, agriculture (A) and energy (E). The technology matrix M and final demand matrices (in billions of dollars) are shown below. A E A 0.5 0.2 5 M = D= E 0.5 0.3 2 and the output for each sector, X, that is needed to satisfy the Find (IM) final demand, D. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (I-M)-1 = (Simplify your answer.) B. The matrix (I - M) is singular.
2. Suppose that the rref of an augmented matrix of a linear system results as 1 0 1 13 0 1 0 21 000 00 (a) What are the leading variables? (b) What are the free variables? (c) What is the corresponding system of equations in terms of the free variables. (d) Write the solutions in vector form.
The input-output matrix for a simplified economy with just three sectors (natural resources, manufacturing, and trade and services) is given below. Natural Resources Manufacturing Trade and Services Natural Resources 0.1045 0.0427 0.0029 Manufacturing 0.0826 0.1087 0.0585 Trade and Services 0.0867 0.1019 0.2031 Suppose the demand (in millions of dollars) matrix is the matrix D, shown below. Find the amount each sector should produce. 451 D= 299 125 Production levels of units from natural resources, units from manufacturing, and units from trade and services are needed. (Round to the nearest whole number as needed.)
Question # 2: Dentists use various amalgams for silver fillings. The matrix shows the percentages expressed as decimals) of powdered alloys used in preparing three different amalgams. Suppose a dentist has 5483 grams of silver, 2009 grams of tin, and 129 grams of copper. How much of each amalgam can be made? Convert it into a system of linear equations and solve using Cramer's rule. PERCENT ALLOY BY WEIGHT Amalgam А в с Silver [0.70 0.72 0.73 Tin 0.26 0.25 0.27 Copper [0.04 0.03 0.00

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In the closed model of Leontief with food, clothing, and housing as the basic industries, suppose that the input-output matrix is A= (1) At what ratio must the farmer, tailor, and carpenter produce in order for equilib- rium to be attained?