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Need help with labor market question: deriving labor demand and wage from labor demand function and labor supply function (!?) @dpflan

OCW Scholar - Principles of Microeconomics
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The labor demand functions is: LD = 34 - 4w, and the labor supply function is: LS = L* + 2w
if L* = 10, then what is the equilibrium wage and labor demand?
Hey @Ackbar, sure, I'll this a try ;)

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\[LD = 34 - 4w\] and \[LS = L* + 2w\] and L* = 10 so \[LS = 10 + 2w\] Now, equate demand and supply so \[LD = LS\] \[ 34 - 4w = 10 + 2w\]
OK, so \[w = (34 - 10) / 6 = 4\]
kk, and LS = 10 + 2*4 = 18
OK!
so what would be elasticity of demand here given the wage? just take the derivative of LD with respect to wage?
\[d{LD} / d{w} * (w^{*} / L^{*}) \]
LD = 34 - 4w, so d(LD) = -4, then -4 * (4 / 18) = -16/18 = -8/9
so that would be inelastic demand for labor at w*

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