Lecture 12: Labour Markets, Wage Discrimination, and International Trade

  1. Four Cases - Because labour is derived from what you need to reproduce
  2. Aggregate of labour demand
  3. OWO: Aggregate of labour supply
  4. International trades


Labour is a DDD: Four Cases

W - Taker - Doesn't affect W

W - Maker - Must W\uparrow W to hire more LL


Example

Supply L=W2L = W-2 production Q=2LQ = 2L demand P=70.25QP = 7-0.25Q

Case 1

PP- Taker P×MP(last worker)=[714Q]×2P×MP(last \ worker)=[7− \frac {1}{4}Q]×2 

WW-Taker =[714(2L)]2= [7-\frac{1}{4}(2L)]2

w=L+2w=L+2 pMP=WpMP = W Labour Demand =14L = 14-L

=14L=L+2=14-L=L+2  L1=6\Rightarrow L_1 =6 w1=8w_1=8


Case 2

Monopoly MR×MP=[712Q]×2=[712(2L)]×2=142LMR×MP=[7− \frac {1}{2}Q]\times 2 = [7− \frac {1}{2}(2L)] \times 2 = 14-2L

WW-Taker: w=L+2w=L+2 MR×MP=wMR \times MP =w 142L=L+214-2L = L+2

Eloss2 in labour market because L2 is lower L2=4, w2=6\Rightarrow L_2 = 4, \ w_2 = 6

Why L1>L2L_1 > L_2? To sell output produced by last worker, PP \downarrow so that output is less valuable


Case 3

P-taker P×MP=14LP \times MP = 14-L same as in 11

Monopsony - Muse ww \uparrow  to L\uparrow L cost of last is \uparrow  μC>w\mu C > w if w=L+2w=L+2 c=wL=L2+2Lc=wL=L^2 + 2L  \Rightarrow μc=2L+2\mu c = 2L +2

Mc=pMP:2L+2=14LMc = p MP : 2L + 2 = 14-L L3=4L_3 =4 w3=6w_3 =6 Not always same as 22 EE loss in labour


Case 4

MP×MP=MC: 142L=2L+2MP \times MP = MC: \ 14-2L =2L +2 L4=3L_4 = 3  w4=5w_4 = 5

Double E-Loss - 1, 2 Monopoly & Monopsony

"Exploitation" - Worth 11, paid 5. Monopoly exploitation. Biggest gap between PMP & P. Toronto Raptors/UofT


Aggregation

4 firms are competitive, 111 monopoly. All are wage takers.

s=10L0.1L2s=10L-0.1L^2  p=120yp=120-y y5Ly-5L w=2Lw=2L p=10p=10 for comp

Monopolist

MP=5MP=5 P=160y P=160-y

MR=1605LMR = 160-5L

MPMR5(1605L)=80025LMPMR - 5(160-5L) = 800-25L

MPMR=W80025L=WMPMR = W \rightarrow 800-25L = W 

LS=825125wLS =\frac {8--}{25}-\frac{1}{25}w

={=L0=L1+L2+L3+L5=L5=1w= \left\{\begin{matrix} = L_0 = L_1 + L_2+L_3+L_5 = \\ L^5 = \frac{1}{w} \end{matrix}\right.


4 Firms

MP=100.2LMP=10-0.2L P=10P=10

pMP=1002LpMP = 100-2L

pMP=w1002L=wpMP = w \rightarrow 100-2L=w

L2=5012wL_2 =50 - \frac{1}{2} w

L3=5012wL_3 =50 - \frac{1}{2} w

L4=5012wL_4=50 - \frac{1}{2} w

L1=5012wL_1=50 - \frac{1}{2} w


Wage Discrimination

Monopolist D=16008PD=1600-8P Full Time LF=2wF100LF =2wF-100

Q=2LQ = 2L LP=2wP60 LP=2wP-60

P=20018QP=200 - \frac{1}{8} Q  MR=20014QMR=200 -\frac{1}{4} Q  MRMP=400LMRMP = 400 - L

=20014(2L)=200 -\frac{1}{4} (2L)

=20012L=200 -\frac{1}{2} L

Lf=2wf100L_f = 2wf -100 w=4014Lw=40 - \frac{1}{4}L

Lp=2wp60L_p = 2wp - 60 μc=4012L\mu c = 40 - \frac{1}{2}L

L=4w160\overline{L} = 4w -160 400L=40+12L400-L = 40 + \frac{1}{2}L

L=240 L=240 MRMP=40012L=180MRMP = 400 - \frac{1}{2} L = 180

\Rightarrow Monopolist needs to ear 18- no matter who they were


International Trade

USA: L=W60L=W - 60  Q=110LQ = \frac{1}{10}L P=1800100Q P=1800-100Q

CAN: L=W40L=W - 40 Q=110LQ = \frac{1}{10}L P=1200100QP=1200-100Q

Case 1

USA: pMP=18010(110L)180LpMP = 180 -10( \frac{1}{10}L)- 180 - L 

W=L+60W = L+60 

180L=L+60180-L=L+60

120=2L120=2L

L=20, W=120L=20, \ W=120

CAN: pMP=12010(110L)120LpMP = 120 -10( \frac{1}{10}L)- 120 - L 

W=L+40W = L+40

120L=L+40120-L=L+40

80=2L80=2L

L=40, W=80L=40, \ W=80

AGGREGATE (Free Trade)

LS?L^S ? 2W100W=50+12L2W-100 \rightarrow W=50 + \frac{1}{2}L

LS=50+12L=WL^S = 50 + \frac{1}{2}L=W

LUSAP=180W+LCANP=L^P_{USA}=180-W+L^P_{CAN}= 120W 120-W

3002W300-2W

LS=LP=W=100L^S = L^P = W=100

LCAN=20L_{CAN}=20,, LUSA=80L_{USA}=80

QUSA=110L=8Q_{USA}= \frac{1}{10} L = 8  QCAN=110L=2 Q_{CAN}= \frac{1}{10} L = 2 

PUSA=1000P_{USA} = 1000 PCAN=1000P_{CAN} =1000

"Factor price equalization theorem"

If labour is mobile, non traded goods will be the same

Law of one price to work, goofs have to be traded internationally non traded will have local markets.


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