Question

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

Answer 1

The labor demand functions is: LD = 34 - 4w, and the labor supply function is: LS = L* + 2w

Answer 2

if L* = 10, then what is the equilibrium wage and labor demand?

Answer 3

Hey @Ackbar, sure, I'll this a try ;)

Answer 4

\[LD = 34 - 4w\] and \[LS = L* + 2w\] and L* = 10 so \[LS = 10 + 2w\]

Now, equate demand and supply so
\[LD = LS\]
\[ 34 - 4w = 10 + 2w\]

Answer 5

OK, so \[w = (34 - 10) / 6 = 4\]

Answer 6

kk, and LS = 10 + 2*4 = 18

Answer 7

OK!

Answer 8

so what would be elasticity of demand here given the wage? just take the derivative of LD with respect to wage?

Answer 9

\[d{LD} / d{w} * (w^{*} / L^{*}) \]

Answer 10

LD = 34 - 4w, so d(LD) = -4, then -4 * (4 / 18) = -16/18 = -8/9

Answer 11

so that would be inelastic demand for labor at w*