mathsperts9

# mathsperts9 - Theorem, show how employment L changes if...

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Mathspert IX. L workers it produces output Q = F ( L ) where F ( : ) is the L = L s ( w ) where the higher the wage paid w; the more the number of workers (i) Simplest case: suppose output Q = AL 1 2 and L = 1 2 [ w R 0 ] : Thus if the w; w ) = pA 1 2 [ w R 0 ] ± 1 2 w 2 [ w R 0 ] : What wage w many workers does the &rm employ? How does employment change if (i) pro- ductivity increases (A), (ii) the reservation wage of workers increases ( R 0 ) : (ii) Output Q = F ( L ) with F increasing and concave, and L = [ w R 0 ] : L L ) = pF ( L ) L [ R 0 + L ] : Thus obtain the necessary condition for optimal employment: pF 0 ( L ) = R 0 + 2 L and check the second order condition for optimality. Using the Implicit Function
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Unformatted text preview: Theorem, show how employment L changes if labour supply increases ( & ) : Use a graph to interpret the necessary condition for optimality [hint: plot three lines pF (L), [R + 2 L=& ] and w=R + L=& with L on the x-axis. Why is it optimal for the marginal revenue product of labour to exceed the wage paid?]. (iii) Output Q = F ( L ) and L = L s ( w ) : Show the necessary conditions for optimality imply optimal employment satis&es pF ( L ) = w [1 + 1 " ] where " = w L s dL s dw is the labour supply elasticity. Explain why this condition di/ers from the competitive solution [where pF ( L ) = w ] : 1...
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## This note was uploaded on 12/31/2011 for the course ECON MR 102 taught by Professor Huyduong during the Winter '11 term at RMIT Vietnam.

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