Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# Suppose the inter-industry flow of the product of two sectors X and Y are given as under. Find the gross output when the domestic demand changes to 12 for X and 18 for Y. - Business Mathematics and Statistics

Sum

Suppose the inter-industry flow of the product of two sectors X and Y are given as under.

 Production Sector Consumption sector Domestic demand Gross output X Y X 15 10 10 35 Y 20 30 15 65

Find the gross output when the domestic demand changes to 12 for X and 18 for Y.

#### Solution

a11 = 15, a12 = 10, x1 = 35

a21 = 20, a22 = 30, x2 = 65

"b"_11 = "a"_11/x_1 = 15/35 = 3/7, "b"_12 = "a"_12/x_2 = 10/65 = 2/13

"b"_21 = "a"_21/x_1 = 20/35 = 4/7, "b"_22 = "a"_22/x_2 = 30/65 = 6/13

The technology matrix is B = [(3/7,2/13),(4/7,6/13)]

I - B = [(1,0),(0,1)] - [(3/7,2/13),(4/7,6/13)]

= [(4/7,-2/13),(-4/7,7/13)], The main diagonal elements are positive

|I - B| = = [(4/7,-2/13),(-4/7,7/13)]

= 4/7 xx 7/13 - (- 4/7) xx ((- 2)/13) => 28/91 - 8/91 = 20/91 > 0

Since the main diagonal elements of I – B are positive and |I – B| is positive the problem has a solution.

adj (I - B) = [(7/13,2/13),(4/7,4/7)]

("I - B")^-1 = 1/|"I - B"| adj (I - B)

= 1/(20/91) [(7/13,2/13),(4/7,4/7)] = 91/20 [(7/13,2/13),(4/7,4/7)]

= 1/20 [(91xx7/13,91xx2/13),(91xx4/7,91xx4/7)]

= 1/20 [(49,14),(52,52)]

X = (I – B)-1D, where D = [(12),(18)]

= 1/20 [(49,14),(52,52)] [(12),(18)]

=> 1/20 [(588 + 252),(624 + 936)]

= 1/20 [(840),(1560)] = [(42),(78)]

Concept: Input–Output Analysis
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