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# LABOR ECONOMICS ECON 150A

UCSB

GPA 3.66

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This 22 page Class Notes was uploaded by Arno Leuschke on Thursday October 22, 2015. The Class Notes belongs to ECON 150A at University of California Santa Barbara taught by K. Bedard in Fall. Since its upload, it has received 60 views. For similar materials see /class/227158/econ-150a-university-of-california-santa-barbara in Economcs at University of California Santa Barbara.

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Date Created: 10/22/15

The Demand for Labor in a Competitive Market As wages rise the demand for labor falls We will prove this in a few days Wag e Labor The Demand for Labor in a Competitive Market Recall that a change in the wage is a movement along the labor demand curve while a shift is caused by a change in the output price a change Wage in an input price other than for labor or a technology change Ld after an output price rise Labor How do firms decide how much labor to hire The fundamental assumption of labor demand theory is that FIRMS ARE PROFIT MAXIMIZERS Firms are always trying to find ways to make larger pro ts The standard OUTPUT interpretation Increase output if the revenue from doing so exceeds the cost Marginal Revenue MR gt Marginal Cost MC The IN PUT interpretation Use more of an input ifthe income from doing so exceeds the cost How do firms decide how much labor to hire More formally a o The marginal product of labor MPL 5 The marginal product of capital MPK A rm can expand or contract output by increasing or decreasing its use of labor or capital However the rm is really interested in the revenue generated by these decisions How do firms decide how much labor to hire The marginal revenue product of labor is MRPL MPL x MR in general MRPL MPL x p in a competitive product market The marginal revenue product of capital is MRPK MPK x MR in general MRPK MPK x p in a competitive product market How do firms decide how much labor to hire In general Increase the amount of labor if MRPL gt MCL Decrease the amount of labor if MRPL lt MCL Keep the same amount of labor if MRPL MCL In a competitive labor market MCL W In a competitive capital market MCK r In a competitive labor market Increase the amount of labor if MRPL gt w Decrease the amount of labor if MRPL lt w Keep the same amount of labor if MRPL w The shortrun versus the longrun Short Run Firms can only alter their variable inputs labor Long Run Firms can alter all inputs Labor Demand in the SHORT RUN For simplicity assume that in the short run LABOR is variable and CAPITAL is fixed Capital KSR Q300 Q200 Q100 Labor With capital xed 39 39 39 39 lllUle labor to L 39 in output This is known as he DECREASING MARGINAL PRODUCTIVITY assumption There are a capital m as more labor is forced to use the same capital stock marginal productivity falls Labor Demand in the SHORT RUN As we saw earlier a firm will increase output or add more labor to the point where the benefit from adding one more unit of labor isjust equal to the cost of doing so M RPL w When both the output Q and labor L markets are competitive MPL X p w w MPL P In other words the productivity ofthe last person hired must equal their real wage Labor Demand in the SHORT RUN Example W 10 per hour p 3 and the last worker hired produces 3 units per hour Should you keep this worker Answer MPL 3 1 333 2 MPL lt 1 P P Since the last worker hired is worth less than he costs you should fire him Labor Demand in the SHORT RUN Capital Q200 o3oo o1oo L1 L2 L3 Labor Since we know that there are diminishing returns to adding more labor when capital is fixed the MPL must be downward sloping Labor Demand in the SHORT RUN MPL wp Labor Labor Demand in the SHORT RUN Since in equilibrium MPL wp then W p MPL And since MPL is falling as MP employment rises labor demand must be W L p increasing as wfalls Labor Optimal amount of labor in the short run In the short run capital is fixed The profit maximizing labor choice is thus given by MPL 3 p Optimal amount of labor in the short run Example Q2K L Z p10 w2 r1 KSR10000 Solution 6 KIM MPL QK 3 212K L 3 3 if 2 6L p P L p 2 pKlA pKlA szl2 L 2 SR 3 L SR 3 LSR ZSR w W w 10210300 2 SR 2 2 2500 Optimal amount of labor in the short run How much profit is earned 7239 pQ wL rKSR 172K 124L12 WL rKSR 10X2gtlt10X50 2X2500 1X10000 5000 Optimal amount of labor in the short run What if p increases to 20 172ng 20210900 2 Labordemand LSR 2 2 10000 w 2 Profit 723920X2X10gtlt100 2gtlt10000 1gtlt10000 10000 Optimal amount of labor in the short run What ifwdeoreases to 1 mm 10210900 2 Labordemand LSRp ZSR1 210000 W 39 Profit 723910gtlt2gtlt10gtlt100 1gtlt10000 1gtlt10000 0 Optimal amount of labor in the short run What is the elasticity of shortrun labor demand 6LSR X w 2p21lt2 X w 77512 6W LSR W3 sz z 2 W 2 Labor Demand in the LONG RUN Both LABOR and CAPITAL are exible in the long run A rm adds more labor andor capital to the point where the benefit from adding one more unit of input isjust equal to the cost of doing so MRPL w and MRPK r When both the output Q and input L and K markets are competitive pMPL w 3 MPL K p pMPK r 2 MPK L p Labor Demand in the LONG RUN Ifwe simply rearrange the equations r MPLw w and 2 i p MPL p MPK MPK r The benefitcost ratio for using one more unit of labor or capital to produce more output must be equal at the pro t maximizing point OthenNise the rm could use less ofone input and more ofthe other input to produce the same output at a lower cost Alternative solution method Alternatively you might want to think about the problem as the following twostage problem 1 The firm chooses the profit maximizing level of output gt the firm increases output until MR MC 2 The rm then chooses the least cost way to produce the profit maximizing level of output Graphically K Isocost Isoquant Notice that the cost minimizing method of producing the pro t maximizing level of output occurs where the slope ofthe isocost is the same as the slope ofthe isoquant In words The slope of the Isocost curve is wr wL rK Cost K Costr wr L o The slope of the Isoquant curve MRS LQ LQ AL AQ AQ AL AK MPK At Q the slope ofthe Isoquant and Iscost curves are the same MRTS 2 7 7 MPK The benefitcost ratio for using one more unit of labor or capital to produce more output must be equal at the profit maximizing point 2 MPL 1 Optimal amount of labor in the long run Example Q2K14L1 p10 w2 r1 Solution W V W w DMPL gt 2MPK 3 L 17 p WK r KIM W 12 Usmg3 L3 3 K 2 K KWL WK 7 L V L r 2r 2K34 pZW leZ 14 2 12 7W 717K 7 2r Subblnglnto LUZ 7 2 L77T 4 Rearranging to isolateL LLR p 3 2rw Optimal amount of capital in the long run 10 4 271413 74 2r 4rzwZ L Subblng L 1nto K KLR r Numerically LLR625 and KLR625 and 7r10x2x5x2572x62571x625625 What if p increases to 20 4 4 p p LLR 2mg 10000 and K W10000 and Ir 20x 2x 5x 2572x1000071x10000 10000 What if w decreases to 1 4 4 p P LLR 7 2M 75000 and K 7 MW 7 2500 and 7r10x2x707x70771x500071x2500 249698 What is the elasticity of long run labor demand Compare this to the short run elasticity of 6ng w 217214 w 773R gtlt 7 3gtlt 2 12 7 aw SR w 7 KSR w2 The longrun elasticity is always greater in absolute value because all inputs are exible Short and Long Run Elasticity Note the labor demand curves are not necessarily straight lines Elasticity Labor demand elasticity is high under the following conditions When the price elasticity of demand for the output produced is high Implications labor demand is more elastic at the firm level than the industry level labor demand is more elastic in the longrun When the other factors of production can easily be substituted for labor When labor costs are a large share of total cost Scale and Substitution Effects K A wage rise 4 4 L SE Sc Since L and K are adjustable in the long run it is important to understand how a change in the price of one input changes the demand for the other input Scale and Substitution Effects The scale and substitution effects are reinforcing for the input whose price changes and offsetting for the input whose price does not change Downward sloping long run LD Labor demand is downward sloping in the longrun because A wage rise leads to substitution away from labor A wage rise lowers the profit maximizing scale of output In other words the Sc and SE ensure a downward sloping labor demand curve in the longrun Sc and SE We know that the Sc and SE go in the same direction for labor is w changes but how do we determine whether the SE or 80 dominates for K Example Q2K 4L P10 12 r1 4 4 LongrunLandKare LLR 2177625 and KLR 457625 04 1 4 Ifw ital LLR 5000 and Km 2500 2113 41Z1Z Ki ScgtSE Let s work through and example Q 4L MK p 120 w 4 r 16KSR 64andafranchisefee 25p Shortrun W 7 W 7 W MPL 3 LSAK 4 3 1134W P P pKSR 743 3 11734743 w pK 3 L amp SR 43 W Numerical Answer 43 13 43 13 717 KER 120 64 591695x437284 LSR 7 w43 443 7 inwLirKSR 725p 4pL14K 4 iwLirKSR 725p 4x 120 x 37284 4 x 6414 7 4 x 37284716 x 647 25 x 120 5965727149136710247 3000 45036 Since profits are positive the profit maximizing level of short run labor demand is 37284 units of labor Lon run MP 9 1MP 3 2MP 1 3 L 1 L K P p NIPK r 43 13 p K 1 L WAK MP w L mK w K w wL 35415 j T j I K 13 p43 I I I 7 r 7p43L13 Subbmgmto1 L7 m gt L 13 W WV p43 3 p2 Reman i to isolate L L gng LR Wt3 W3ZrlZ p Solvm for K K 7 g LR WlZr3Z Numerical Answer Z Z 7 p 7 120 714400 7 LLR wzizriiz 4321612 8X4 7450 Z Z Km P i14 400 1125 WlZrKZ 4121632 64X2 7r pQ7wL7rK725p 4pL MK 7wL7rK725p 4x120x450 x1125 74x450716x1125725x120 7200718007180073000 600 Since profits are positive the profit maximizing level of long run labor demand is 450 units of labor and the longrun capital demand is 1125 units What if p increases to 130 p lzK ij 7130 64 7 65855X4 6 5 LSR m 4m 41484 w 7r pQ7wL7rKSR 7 25p 4pL l K Sj 7wL7rKSR 7 25p 4x 130 x 41484 x 64 M 7 4x 41484716x 647 25x 130 6637647165936710247 3250 70428 Since profits are positive the profit maximizing level of short run labor demand is 41484 units of labor 20 What if p increases to 130 Z Z p 130 16900 LLR WKZrlZ 4321612 8X4 5283913 Z Z Km p 130 716900 13203 wlZrKZ 4121632 64x2 7 inwLirK725p 4pL MK M iwLirK725p 4x130x52813 x1320 74x52813716x13203725x130 8448127211253721124873250 97311 Since profits are positive the profit maximizing level of long run labor demand is 52813 units of labor and the longrun capital demand is 13203 units What if w increases to 6 21721 SR 43 43 w 6 L p43ngf 1204364 3 59189x4 09 7 inwLirKSR 725p 4pL14K4 iwLirKSR 725p 4x 120 x 21721 x 64W 7 6x 21721716 x 647 25 x120 521271303267102473000 711526 Since profits are negative the profit maximizing level of shortrun labor demand is 0 units of labor 21 What if w increases to 6 2 2 7 p 7 120 7 14400 7 LLR 7 WKZrlZ 7 6321612 7147X4 7 244399 2 1202 14400 K 9184 LR wlZrKZ 6121632 64X 245 7pgiwLirK725p4le4KWiwLirK725p 4gtlt120gtlt2449 A x9184 4 76x2449716gtlt9184725gtlt120 587820 7146947146944 7 3000 76064 Since profits are negative the profit maximizing level of long run labor demand is 0 units of labor and the longrun capital demand is 0 units What is the elasticity of labor demand 8L 43K13 Shortrun vSR xLlexwi43 SR P SR WM 6L w 322 w Long run 77m a xg77w52r12XT7732 w32r12 The longrun elasticity is always greater in absolute value because all inputs are flexible 22

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