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s: Goods and Services. Each year, Goods sells 80% of its

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald ISBN: 9780321982384 49

Solution for problem 1E Chapter 1.6

Linear Algebra and Its Applications | 5th Edition

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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

Linear Algebra and Its Applications | 5th Edition

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Problem 1E

Suppose an economy has only two sectors: Goods and Services. Each year, Goods sells 80% of its output to Services and keeps the rest, while Services sells 70% of its output to Goods and retains the rest. Find equilibrium prices for the annual outputs of the Goods and Services sectors that make each sector’s income match its expenditures. Example 1:Suppose an economy consists of the Coal, Electric (power), and Steel sectors, and the output of each sector is distributed among the various sectors as shown in Table 1 on page 50, where the entries in a column represent the fractional parts of a sector’s total output. The second column of Table 1, for instance, says that the total output of the Electric sector is divided as follows: 40% to Coal, 50% to Steel, and the remaining 10% to Electric. (Electric treats this 10% as an expense it incurs in order to operate its business.) Since all output must be taken into account, the decimal fractions in each column must sum to 1.Denote the prices (i.e., dollar values) of the total annual outputs of the Coal, Electric, and Steel sectors by pC, pE, and pS, respectively. If possible, find equilibrium prices that make each sector’s income match its expenditures.

Step-by-Step Solution:
Step 1 of 3

Solution:-Step1Given that Goods and Services. Each year, Goods sells 80% of its output to Services and keeps the rest, while Services sells 70% of its output to Goods and retains the rest.Step2To findFind equilibrium prices for the annual outputs of the Goods and Services sectors that make each sector’s income match its expenditures.Step3Represent the data in the following tableGoodsServices0.20.7Goods0.80.3ServicesEach column represents the fraction of output from one branch to the others. For example the second column say that services sell 0.7 of its output to goods and retains the rest 0.3 of its output to itself.Let be a price for goods and let be a price for services. Goods spends0.2 andServices spends0.8To balance the income and outcome we need0.20.8Rewrite the equation as0.80.8It is actually the same equation with the solution It follows that the prices can be chosen as followsThe only condition is that

Step 2 of 3

Chapter 1.6, Problem 1E is Solved
Step 3 of 3

Textbook: Linear Algebra and Its Applications
Edition: 5
Author: David C. Lay; Steven R. Lay; Judi J. McDonald
ISBN: 9780321982384

Since the solution to 1E from 1.6 chapter was answered, more than 343 students have viewed the full step-by-step answer. This full solution covers the following key subjects: output, sector, its, electric, sectors. This expansive textbook survival guide covers 65 chapters, and 1898 solutions. Linear Algebra and Its Applications was written by and is associated to the ISBN: 9780321982384. The answer to “Suppose an economy has only two sectors: Goods and Services. Each year, Goods sells 80% of its output to Services and keeps the rest, while Services sells 70% of its output to Goods and retains the rest. Find equilibrium prices for the annual outputs of the Goods and Services sectors that make each sector’s income match its expenditures. Example 1:Suppose an economy consists of the Coal, Electric (power), and Steel sectors, and the output of each sector is distributed among the various sectors as shown in Table 1 on page 50, where the entries in a column represent the fractional parts of a sector’s total output. The second column of Table 1, for instance, says that the total output of the Electric sector is divided as follows: 40% to Coal, 50% to Steel, and the remaining 10% to Electric. (Electric treats this 10% as an expense it incurs in order to operate its business.) Since all output must be taken into account, the decimal fractions in each column must sum to 1.Denote the prices (i.e., dollar values) of the total annual outputs of the Coal, Electric, and Steel sectors by pC, pE, and pS, respectively. If possible, find equilibrium prices that make each sector’s income match its expenditures.” is broken down into a number of easy to follow steps, and 208 words. This textbook survival guide was created for the textbook: Linear Algebra and Its Applications , edition: 5. The full step-by-step solution to problem: 1E from chapter: 1.6 was answered by , our top Math solution expert on 07/20/17, 03:54AM.

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s: Goods and Services. Each year, Goods sells 80% of its