Linear Algebra : Leontief Input-Output Model and Real-World Applications

1. Why did Leontief use linear algebra techniques to create his model? Can you think of alternative methods?
2. What are the main strengths of his model?
3. Does it have any limitations (that you can think of)?
4. How might the Input-Output model be useful in the real world? (In other words, would anyone except an Economist be interested in the results?)

1. Why did Leontief use linear algebra techniques to create his model? Can you think of alternative methods?
The elementary multiplier concept claims only to explain how an increase in final demand, such as a step up in the level of government spending on goods and services, will affect the level of aggregate Gross Domestic Product. The multiplier neglects the obvious limitations involved in working with such national income aggregates as GDP and government spending without regard to the composition of government spending and output. For example, the multiplier will not tell us what will happen if the government shifts $50 billion from military spending to the construction of urban transportation networks or to public housing. Such a shift would obviously stimulate the housing industry. It might be bad for electronics. But would it cause an increase or a decrease in the demand for steel? Nobel Laureate Wassily Leontief in the 1930's, developed the model to analyze the effects of shifts in the composition of government spending on the output of different industries. This procedure for addressing ...

Solution Summary

The Leontief Input-Output Model and Real-World Applications are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

A closed model for an economy identifies government, the profit sector, the nonprofit sector, and households as its industries. Each unit of government output requires 0.4 unit of government input, 0.3 unit of profit sector input, 0.3 unit of nonprofit sector input, and 0.4 unit of households input. Each unit of profit sector ou

Please help. I always have a hard time with LinearAlgebra. What's the difference between mapping from R3 into R2 and mapping from R2 into R3?
Why is the following not a linear transformation from R3 into R2?
L(x) = (1 + x1, x2)^T
And why is this one not a linear transformation from R2 into R3?
L(x) = (x1, x2, 1)^T
Th

If factor-intensity reversals were indeed prevalent in the real world, how might this fact be used to explain the Leontief paradox? If this explained the paradox, would it suggest that any given U.S. trading partner stood a better chance of conforming to Heckscher-Ohlin than did the United States (i.e., will a factor intensity r

What similarities and differences do you see between the functions andlinear equations studied in Ch. 3? Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate.

Let R be the field of real numbers, and let D be the function on 2x2 matrices over R with values in R, such that D(AB)=D(A)D(B) for all A, B. Suppose that D([0,1;1,0])=/D([1,0;0,1]).
Prove that:
1. D([0,0;0,0])=0
2. D(A) = 0 if A^2=0

I need to show a linear equation and explain what it represents.
I need to state what the "x" and "Y" in equation represents
I have to be able to evaluate the equation for at least two variables and provide reference where you got the equation from.
Part 2: Using the Library, web resources, and/or other materials, find a r

1) Use the input-output matrix and the Closed Model to find the ratio of yams to pigs produced.
2) Find [I-A]. Solve [I-A] [X]=0
Yams Pigs
Yams 1/4 1/2
Pigs 3/4 1/2

With referrence to the last solutions u posted to me,may you please check no 1 I have a different solution from my workings.I not sure which one is correct,but I think mine might be.If so may u please edit the document because I failed to do so.I will use this over and over.