7
votes
Aggregation of the closure property of a production set
Doing this more abstractly, let $Y_j\subseteq\mathbb{R}^n$ be a production set for $j=1,\ldots,J$ and let
$$Y=Y_1+Y_2+\cdots+Y_J=\{y_1+y_2+\cdots+y_J|y_j\in Y_j, j=1,\ldots,J\}$$
be the aggregate ...
- 13.5k
5
votes
Accepted
Why the definition of productive economy in Leontief Open Model is such?
This is a specific terminology employed in the literature on Leontief model. Productive here means that all sectors must be profitable (do not confuse it with notions of productivity used elsewhere in ...
- 57.7k
4
votes
Accepted
What does the Leontief Inverse represent? (Intuitive Meaning or Real World Concept)
Something you didn't mention is that
$x = Ax + y$
means that to produce one unit of $x$, you use $A$ unit of $x$. E.g. you need electricity to produce electricity.
Under the condition that $1>|A|...
- 1,435
4
votes
Aggregation of the closure property of a production set
For a fully overview on the conditions for the sum of closed sets to be closed, see this note of Kim Border
Recession cones
I'll be working with subsets of $\mathbb{R}^n$. Let's start with some ...
- 12.5k
4
votes
Accepted
How could you partition Household Food Expenditures into Producing Industries?
You should try to avoid mixing data sets unless you have a good way to bridge them. There are very precise methodologies used to construct each data set and mixing them can lead to nonobvious problems....
- 9,355
4
votes
What is the difference between personal consumption expenditure price and PCE quantity?
Personal consumption expenditure (PCE) is the primary measure of consumer spending on goods and services in the U.S. economy. It accounts for about two-thirds of domestic final spending, and thus it ...
- 1,467
3
votes
Accepted
Why do the BEA's Use and Supply Tables have Industries (and not products) on the Rows?
Short Answer
The Use and Supply tables do not have industries on both rows and columns. For example, as shown in the screenshot below, the Supply table has commodities on the rows and the industries ...
- 9,355
2
votes
What does the Leontief Inverse represent? (Intuitive Meaning or Real World Concept)
The series <I + A + A^2 + A^3 + ... + A^N> converges on the Leontief inverse (I-A)^(-1) as N approaches infinity. In this format, I can be thought of as initial demand for a given product, A ...
- 21
2
votes
What does the Leontief Inverse represent? (Intuitive Meaning or Real World Concept)
What intuition can the mathematical concept of an inverse (function, matrix) have?
In a single-input monotonic production function $F(x) = q \implies x= F^{-1}(q)$ the operator $F^{-1}$ is the ...
- 33.9k
1
vote
Accepted
No profits if labour is the only input into production?
I'm studying the Richardian model now - it says that, if labour is the only input into production, there are no profits, so workers receive the full value of their output - i can't wrap my head around ...
- 57.7k
1
vote
Share of domestic and foreign monetary flows between sectors of a country
The exports and imports in an input-output analysis should correspond to imports and exports as components of GDP so you can use those or some measures derived from them.
For example, trade as a $\%$ ...
- 57.7k
1
vote
Accepted
How to estimate the labor time required to produce all necessities in a given economy (assuming all goods/services are produced domestically)?
Open question: how would you best make such an estimate?
Normally, if you would not care about closing the economy, such estimate would be simply done by calculation of real wages per hour and then ...
- 57.7k
1
vote
Optimal Production Input in Relation to Cost Minimization Problem
I`d propose you to follow these steps:
Set up the minimization cost problem (i.e. for a given output quantity $y$ minimize costs):
\begin{align}
\min_{H,L,K}& \quad sH + wL + rK \tag{1} \label{1}...
- 354
1
vote
Accepted
How to prove that a concave production imply that the input requirement sets are convex?
Start with definitions:
Production (possibilities) set: $Y$ which you know is convex
Input requirement set: $V(y)=\{\mathbf{x}:(y,−\mathbf{x})∈Y\}$
On page 7. you can see: $\mathbf{y}\in Y$ and $\...
- 939
1
vote
How to build a Social Accounting Matrix from an Input-Output Table?
IOTs are usually derived from Supply and Use tables, which have an industry by commodity format. If you used these to derive your IOT, then you can use those to build your SAM, though note you need ...
- 251
1
vote
Quasi Fixed Input
Quasi-fixed labour costs are typically those associated with the number of workers rather than the number of hours they work, so things like
recruitment costs
training costs
Commonly they are seen ...
- 4,765
1
vote
Accepted
Is the capital-output ratio in developing countries low or high?
The key to the answer is good data on Capital. There is a project (KLEMS), which is computing harmonised (i.e. comparable) information on capital, labour, energy, etc for many countries. At the moment ...
- 8,611
1
vote
What would the determinant of the input-output matrix represent? What is the intuition?
Your conjecture seems unlikely. For example the unit matrix would show an economy where no new goods can be produced (it takes 1 unit of something to make 1 unit of that same thing). Yet the ...
- 29.6k
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