Section 4. Static Labor Demand

Transcription

1 42 4. STATIC LABOR DMAND Reference: Borjas, Chater 4 Production function Section 4. Static Labor Demand (1) q = f( }{{} emloyees in ersons Marginal roduct MP = q MP K = q K, }{{} K ) caital Average roduct ˆ= roductivity AP = q AP K = q K Production function for K = constant:

2 4. STATIC LABOR DMAND 43 Profit maximization (2) Π = q rk for,r, given erfectly cometitive firm Value marginal roduct V MP = MP Value average roduct V AP = AP Max Π yields First Order Condition (FOC): Π = MP = 0 V MP = MP! = Second Order Condition: V MP declining i.e. > }{{} max of MP Caital constant: Labor Demand in the short run No adjustment in caital imlies short run demand curve: ( ) ( ) SR = MP 1

3 44 4. STATIC LABOR DMAND actually inverse of MP function in real age rovided rice is constant lasticity of labor demand in short run δ SR = SR SR SR SR mloyment decision in the long run: Long-run labor demand hen the firm s caital stock is not fixed Isoquants: f(, K) = q combinations of and K resulting in the same level of outut q q 1 > q 0 Sloe of isoquant: f dk d = f K = MP MP K marginal rate of technical substitution

4 4. STATIC LABOR DMAND 45 Profit maximization imlies cost minimization Iso cost curve: C = + rk ith r: rice of caital combinations of and K resulting in the same costs C K = C r r Cost minimization yields combination (, K) in P ith r = MP MP K = MP K r or ut differently MP i.e. get the same additional outut for each uro. or ut differently MP = r MP K i.e. ay the same for an additional unit of outut roduced by using more labor or by using more caital.

5 46 4. STATIC LABOR DMAND Profit maximization: max {,K} π = q r K given, r, s.t. q = f(, K) FOC: π = MP = 0 = MP π K = MP K r = 0 r = MP K conditions for rofit maximization Profit max: = MC(marginal cost) r = MP MP K imlies condition for cost minimization Thus, rofit maximization cost minimization Long-run demand for labor Ho does emloyment react in resonse to a fall in the age fall in age causes fall in MC MC 0 MC 1 K K 1 0 q 1 q 0 q 1 q r 1 r q0 Increase from 0 to 1 can be decomosed into scale and substitution effect - Scale effect results from increase in q : q 0 q 1

6 4. STATIC LABOR DMAND 47 K scale effect substitution effect 0 r 1 r It is clear that < 0 K? because because both scale effect and substitution effect go into the same direction ( ) K > 0 and subst. ( ) K < 0 scale The long run labor demand curve is steeer than the short run short run General rincile in economics: agents can resond more easily to changes hen facing feer constraints (in short run cannot change caital inut!) long run

7 48 4. STATIC LABOR DMAND lasticity of Substitution: σ Isoquants K K K Perfect substitutes σ = Substitution ossible but becomes increasingly difficult 0 < σ < (Cobb Douglas: σ = 1) Perfect comlements (limitational technology σ = 0 σ = K MP MP K MP = Percent change in (K ) K MP K Percent change in ( r ) because MP MP K = r by cost minimization The larger σ is, the larger is the substitution effect

8 4. STATIC LABOR DMAND 49 Scale effect deends on outut demand Let η be elasticity of outut demand q d q = η < 0 monoolistic cometition then long run labor demand elasticity is (under constant returns to scale) η = = η s }{{} σ(1 s ) }{{} < 0 scale effect substitution effect here s = + rk = labor share in costs This formula, hich is generally true, reflects Marshall s rules of derived demand: Labor demand is more elastic, the greater the elasticity of substitution σ the elasticity of demand for outut η in absolute value labor s share in total costs the suly elasticities of other factors of roduction, such as caital

9 50 4. STATIC LABOR DMAND Aside: Linear homogeneous roduction function y = F (, K) λy = F (λ, λk) uler Theorem: 1 y = F + K F K (Adding u) 1 = F y + K F K y (scale elasticity of roduction) = s L + s K Define: F = F/ and F K = F/ K If F (, K) is linear homogeneous, then F (, K) and F K (, K) are homogeneous ith degree zero (zero homogeneous). This means F (, K) = F (λ, λk) F K (, K) = F K (λ, λk) Analogous to the uler Theorem, the folloing holds also for zero homogeneous functions: 0 = 0 F (, K) = L F LL (, K) + K F K (, K) 0 = 0 F K (, K) = L F KL (, K) + K F KK (, K) This imlies: F = K F K and F KK = K F K = K F K Finally, the elasticity of substitution is: σ = d ln (K ) d ln ( F F K ) = F F K y F K

10 4. STATIC LABOR DMAND 51 quilibrium in the Labor Market and Minimum Wages Macro Persective: Homogeneous labor, quilibrium in the labor market rents of firms S rents of emloyees D A statuatory (obligatory) minimum age alies to the hole economy. m rents of firms elfare loss S m < Unemloyment rents of emloyees m D

11 52 4. STATIC LABOR DMAND More realistic case: Minimum age only alies for art of the economy (this is the covered sector). In the other art (uncovered sector), there is age flexibility, so there ill be adjustment to the labor market equilibrium in this sector. m A S 1 A S 2 S 2,m D 1 D 2 m,1 1 2 m,2 (a) Sector 1 ith minimum age (b) Sector 2 ithout minimum age In Sector 1, the age increases and emloyment decreases. Therefore, labor suly increases in sector 2 and age decreases and emloyment increases Marginal roduct in sector 2 is smaller than in sector 1, that means the elfare loss in sector 1 is bigger than the elfare increase in sector 2.

12 4. STATIC LABOR DMAND 53 Monosony in the labor market Also, ith market oer of the firm in the labor market (here single monosony), rofit maximization imlies Value marginal roduct = Marginal cost of labor i.e. P q = (1 + η, ) > age marginal cost of labor m S m 0 D (P q ) 0 m 0 emloyment under monosony < equilibrium emloyment Introduction of a minimum age m beteen 0 and m increases the emloyment emloyment under minimum age m > 0 since marginal cost of labor is no equal to m and not (1 + η, ) = m at 0. Reasons, hy emloyment effects of minimum ages may not be negative or even ositive Card and Krueger Myth and Measurement, 1994.