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“最終需要·最終産出 模型”을 통한 産業聯關 및 乘數效果

金鎬彦

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Abstract

Nowadays, the two general relations between two different input requirements matrices(Γ ? and Γ g ) and between two output requirements matrices(C ? and C g ) were clarified by Gim(1998, 2005). Moreover, a new concept of??the output requirements matrix for output??C g , based on the decomposition by factors of the Leontief inverse C ? , was also developed by Gim and Kim(2005). From the research results mentioned above, the new different models, the output-output and final demand-final output models, were built through the mutual relation between final demand(?), total output(χ), and final output(ο). The study objectives of this paper can be summarized as follows. (1) We intend to show the mutual relation between input-output, output-output, and final demand-final output among the variables final demand(?), gross output(χ), and final output(ο), and then we can derive the relation equations in determining the characteristic relations and models. (2) We draw the impact and sensitivity coefficients for measuring the forward and backward linkage effects through the final demand-final output model and define various types of multipliers baced on the matrix C g C ? . The output multiplier, on the basis of C g C ? , for sector j, denoted by ? ∨ο j and shown as Eqs. (12) and (13), is defined as the final output requirements in all endogenous sectors of the economy that are needed to support a unit of final demand of sector j. The employment multiplier, also based on C g C ? , for sector j, ? ∨L j , shown as Eqs. (15) and (16), is defined as the ratio of total employment effects(total employment changes) in all sectors of the economy resulting from one unit change for sector j final demand, to the direct employment effect for sector j output(or input). The income multiplier, which is based on C g C ? , for sector j, denoted by ? ∨Y j and shown as Eqs. (18) and (19), is defined as the ratio of total income effects(total income changes) in all sectors of the economy resulting from one unit change of sector j final demand, to the direct income effect for sector j output(or input).

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Nowadays, the two general relations between two different input requirements matrices(Γ ? and Γ g ) and between two output requirements matrices(C ? and C g ) were clarified by Gim(1998, 2005). Moreover, a new concept of??the output requirements matrix for output??C g , based on the decomposition by factors of the Leontief inverse C ? , was also developed by Gim and Kim(2005). From the research results mentioned above, the new different models, the output-output and final demand-final output models, were built through the mutual relation between final demand(?), total output(χ), and final output(ο). The study objectives of this paper can be summarized as follows. (1) We intend to show the mutual relation between input-output, output-output, and final demand-final output among the variables final demand(?), gross output(χ), and final output(ο), and then we can derive the relation equations in determining the characteristic relations and models. (2) We draw the impact and sensitivity coefficients for measuring the forward and backward linkage effects through the final demand-final output model and define various types of multipliers baced on the matrix C g C ? . The output multiplier, on the basis of C g C ? , for sector j, denoted by ? ∨ο j and shown as Eqs. (12) and (13), is defined as the final output requirements in all endogenous sectors of the economy that are needed to support a unit of final demand of sector j. The employment multiplier, also based on C g C ? , for sector j, ? ∨L j , shown as Eqs. (15) and (16), is defined as the ratio of total employment effects(total employment changes) in all sectors of the economy resulting from one unit change for sector j final demand, to the direct employment effect for sector j output(or input). The income multiplier, which is based on C g C ? , for sector j, denoted by ? ∨Y j and shown as Eqs. (18) and (19), is defined as the ratio of total income effects(total income changes) in all sectors of the economy resulting from one unit change of sector j final demand, to the direct income effect for sector j output(or input).

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Available abstract

Nowadays, the two general relations between two different input requirements matrices(Γ ? and Γ g ) and between two output requirements matrices(C ? and C g ) were clarified by Gim(1998, 2005). Moreover, a new concept of??the output requirements matrix for output??C g , based on the decomposition by factors of the Leontief inverse C ? , was also developed by Gim and Kim(2005). From the research results mentioned above, the new different models, the output-output and final demand-final output models, were built through the mutual relation between final demand(?), total output(χ), and final output(ο). The study objectives of this paper can be summarized as follows. (1) We intend to show the mutual relation between input-output, output-output, and final demand-final output among the variables final demand(?), gross output(χ), and final output(ο), and then we can derive the relation equations in determining the characteristic relations and models. (2) We draw the impact and sensitivity coefficients for measuring the forward and backward linkage effects through the final demand-final output model and define various types of multipliers baced on the matrix C g C ? . The output multiplier, on the basis of C g C ? , for sector j, denoted by ? ∨ο j and shown as Eqs. (12) and (13), is defined as the final output requirements in all endogenous sectors of the economy that are needed to support a unit of final demand of sector j. The employment multiplier, also based on C g C ? , for sector j, ? ∨L j , shown as Eqs. (15) and (16), is defined as the ratio of total employment effects(total employment changes) in all sectors of the economy resulting from one unit change for sector j final demand, to the direct employment effect for sector j output(or input). The income multiplier, which is based on C g C ? , for sector j, denoted by ? ∨Y j and shown as Eqs. (18) and (19), is defined as the ratio of total income effects(total income changes) in all sectors of the economy resulting from one unit change of sector j final demand, to the direct income effect for sector j output(or input).

Key concepts: Final demand, Multiplier (economics), Input/output, Input–output model, Gross output, Linkage (software), Relation (database), Mathematics

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