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101_F07_HO_2+ - K 2 L 2> 2 K 2 L 2 = 2 F K;L IRS 3:F K;L...

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ECN 101 Fall 07 Shaofeng Xu Supplement to Handout 2 Oct 8, 2007 If a production function Y = F ( K; L ) : . F (2 K; 2 L ) = 2 F ( K; L ) () F ( : ) constant return to scale(CRS) . F (2 K; 2 L ) > 2 F ( K; L ) () F ( : ) increasing return to scale(IRS) . F (2 K; 2 L ) < 2 F ( K; L ) () F ( : ) decreasing return to scale(DRS) Examples: consider the following production functions: 1 :F ( K; L ) = K 1 = 3 L 2 = 3 we have F (2 K; 2 L ) = (2 K ) 1 = 3 (2 L ) 2 = 3 = 2 1 = 3+2 = 3 K 1 = 3 L 2 = 3 = 2 K 1 = 3 L 2 = 3 = 2 F ( K; L ) ) CRS 2 :F ( K; L ) = K 2 L 2 we have F (2 K; 2 L ) = (2 K ) 2 (2 L ) 2 = 2 4 K 2 L 2 = 16
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Unformatted text preview: K 2 L 2 > 2 K 2 L 2 = 2 F ( K;L ) ) IRS 3 :F ( K;L ) = K 1 = 3 L 1 = 3 we have F (2 K; 2 L ) = (2 K ) 1 = 3 (2 L ) 1 = 3 = 2 2 = 3 K 1 = 3 L 1 = 3 < 2 K 1 = 3 L 1 = 3 = 2 F ( K;L ) ) DRS 4 :F ( K;L ) = 2 K + 3 L we have F (2 K; 2 L ) = 2(2 K ) + 3(2 L ) = 2(2 K + 3 L ) = 2 F ( K;L ) ) CRS 1...
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