Input-Output Analysis, Linear Programming and Modified Multipliers

in a specific sector, but the multipliers in LP formulation are updated accordingly when
additional restrictions are added on the sector’s production directly. As mentioned
earlier, if researchers and policy makers want to recover economic loss from exogenous
production restrictions, the modified multiplier should be used. Otherwise economic
boosting policy tends to be overestimated.

This paper consists of the following five parts. Section 2 discusses the IO analysis
and multipliers, and section 3 shows how to derive multipliers from the LP formulation
analytically. Section 4 contains extension of the LP formulation with the additional
constraints and how to derive the modified multipliers responding to this change. Section
5 includes a numerical example and empirical application, and section 6 concludes the
findings.

Input-Output Analysis and Multipliers

For an economy of n sectors (industries) the standard IO model is represented by

X = Y + AX, where X is the output vector, Y is the final demand vector, and A is the

^xij

direct requirement matrix, which elements, a_ij, are calculated as a_jj = —, where x_jj is the
xj

transaction between sector j and j, and x_j is the sectoral output which is x_j = ∑ x_jj . This
j

relation indicates that the sum of output X equals to the direct uses in final demand Y and
its indirect uses in intermediate production AX. The solution can be obtained by rewriting
as:

(1)     X=(I-A)^-1Y,

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