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Let the representative vector of goods that a consumer purchases be denoted as X.
Utility is a function of these commodities: (1) where (2) is a vector of goods used to produce and is time (usually assumed scalar but allowed to be a vector in Becker, 1965).
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Let C h = (Ch,1, …, Ch,m) be the consumption vector of m goods by a household of type h and P = (p1, …, p m ) the corresponding price vector.
With a slight abuse of notation I reserve p for the price (row) vector of the produced goods and services-the price vector of Section 2 becoming ( p w r ).
({mathbf{N}}_{{mathbf{I}}}) is a vector denoting the imports of goods and services from other regions of Japan, and ({mathbf{N}}_{{mathbf{W}}}) indicates the transportation of waste resources from other regions of Japan to Kyoto.
({mathbf{E}}_{{mathbf{I}}}) is a vector denoting the international exports of goods and services, and (text{mathbf{E}}_{{mathbf{W}}}) indicates the transport of waste resources from Kyoto to foreign countries.
({mathbf{M}}_{{mathbf{I}}}) is a vector denoting the international imports of goods and services, and ({mathbf{M}}_{{mathbf{W}}}) indicates the transportation of waste resources from foreign countries to Kyoto.
The wealth indicator W is a composite asset-based index of wealth, computed as the first component of a vector of assets and durable goods.
We currently portray the sialotranscriptome of Culex tarsalis, a North American bird feeding mosquito [ 30], and, like C. pipiens, a good vector of West Nile virus [ 31].
In fact, when the vector x is a linear combination of P vectors of the dictionary F, then the vector y is a linear combination of P vectors of the dictionary Φ, and the quasi-orthogonality of the vectors of Φ allows to favor the choice of good vectors (the others being orthogonal to y).
ϕ i is a Nash equilibrium strategy given by Roberts ([1979a, 1979b]) as ϕ i = π i − 1 − 2 δ i N − 1 ( ∑ j ∈ N ψ j − γ ), ∀ i ∈ N. Let π = ( π 1, …, π N ) be a vector of MRSs for the public good and Π be its set.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com