University:
University of Pennsylvania
Course:
ECON 0430 | Labor Economics
Academic year:

2020
Views:

448

Pages:

15
Author:

esfredint7qo

Outline Introduction Frisch Elasticity of Labor Supply Frisch Elasticity of Labor Supply Outline Introduction Introduction Frisch Elasticity of Labor Supply Outline Introduction Type of Supply Function of Labor I Marshallian labor supply. Hold Income constant. Frisch Elasticity of Labor Supply Outline Introduction Type of Supply Function of Labor I Marshallian labor supply. Hold Income constant. I Hicksian labor supply. Hold utility level constant. Frisch Elasticity of Labor Supply Outline Introduction Type of Supply Function of Labor I Marshallian labor supply. Hold Income constant. I Hicksian labor supply. Hold utility level constant. I Frisch labor Supply. Hold the marginal utility of wealth constant. Frisch Elasticity of Labor Supply Outline Introduction Frisch Elasticity The Frisch labor supply Elasticity ( constant marginal utility of wealth) is defined as ∂n w ηλ = kλ (1) ∂w n Frisch Elasticity of Labor Supply Outline Introduction Simple Standard Consumer Problem max ct ,at+1 ,n ∞ X β t U(ct , nt ) (2) t=0 subject to: ct + at+1 = (1 + r )at + wt nt I multiplier λt β is the discount factor, at is the household asset in the beginning of period t, and nt , units of labor. Frisch Elasticity of Labor Supply (3) Outline Introduction FOC’s The FOC’s are: Uc t = λ t (4) −Unt = λt wt (5) λt = β(1 + r )λt+1 (6) Frisch Elasticity of Labor Supply Outline Introduction FOC’s Notice (4) and (5) are in function of λ and w: ∂U(c(λ, w ), n(λ, w )) =λ ∂c (7) ∂U(c(λ, w ), n(λ, w )) = −λw ∂n (8) Frisch Elasticity of Labor Supply Outline Introduction Computing Frisch Elasticity Taking derivative of (4) and (5) with respect to w, we have Ucc ∂c ∂n + Ucn =0 ∂w ∂w ∂c ∂n + Unn = −λ ∂w ∂w Notice this is a system of 2 equations and two unknowns. Unc Frisch Elasticity of Labor Supply (9) (10) Outline Introduction Computing Frisch Elasticity Solving for ∂n ∂w we have: ∂n λUcc = 2 ∂w [Ucn − Unn Ucc ] (11) Replacing λ from (5) we have − Un Ucc ∂n = 2 w ∂w [Ucn − Unn Ucc ] Frisch Elasticity of Labor Supply (12) Outline Introduction Computing Frisch Elasticity Using the last expression we have that the Frisch labor supply elasticity is ηλ = Un n[Unn − 2 Ucn Ucc ] Frisch Elasticity of Labor Supply (13) Outline Introduction Example: Separable Utility Consider the following utility function 1 U(c, n) = ln(c) − α FOC’s: n1+ ν 1 + ν1 1 =λ c 1 αn ν = λw Frisch Elasticity of Labor Supply (14) (15) (16) Outline Introduction Example: Separable Utility The labor supply is given by n=( w ν ) αc (17) The Fischer elasticity is given by ηλ = ν Frisch Elasticity of Labor Supply (18) Outline Introduction Example: Non Separable Utility Consider the another utility function U(c, n) = (c γ (1 − n)1−γ )(1−σ) 1−σ (19) The Frisch Elasticity is given by ηλ = 1 − n 1 − γ(1 − σ) [ ] n σ Frisch Elasticity of Labor Supply (20)

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