# 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

#### Labour is a DDD: Four Cases

W - Taker - Doesn't affect W

W - Maker - Must ﻿$\uparrow W$﻿ to hire more ﻿$L$﻿

### Example

Supply ﻿$L = W-2$﻿ production ﻿$Q = 2L$﻿ demand ﻿$P = 7-0.25Q$﻿

#### Case 1

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

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

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

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

#### Case 2

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

﻿$W$﻿﻿$-$﻿Taker: ﻿$w=L+2$﻿ ﻿$MR \times MP =w$﻿ ﻿$14-2L = L+2$﻿

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

Why ﻿$L_1 > L_2$﻿? To sell output produced by last worker, ﻿$P \downarrow$﻿ so that output is less valuable

#### Case 3

P-taker ﻿$P \times MP = 14-L$﻿ same as in ﻿$1$﻿

Monopsony - Muse ﻿$w \uparrow$﻿ to ﻿$\uparrow L$﻿ cost of last is ﻿$\uparrow$﻿ ﻿$\mu C > w$﻿ if ﻿$w=L+2$﻿ ﻿$c=wL=L^2 + 2L$﻿ ﻿$\Rightarrow$﻿ ﻿$\mu c = 2L +2$﻿

﻿$Mc = p MP : 2L + 2 = 14-L$﻿ ﻿$L_3 =4$﻿ ﻿$w_3 =6$﻿ Not always same as ﻿$2$﻿ ﻿$E$﻿ loss in labour

#### Case 4

﻿$MP \times MP = MC: \ 14-2L =2L +2$﻿ ﻿$L_4 = 3$﻿ ﻿$w_4 = 5$﻿

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, 1﻿$1$﻿ monopoly. All are wage takers.

﻿$s=10L-0.1L^2$﻿ ﻿$p=120-y$﻿ ﻿$y-5L$﻿ ﻿$w=2L$﻿ ﻿$p=10$﻿ for comp

#### Monopolist

﻿$MP=5$﻿ ﻿$P=160-y$﻿

﻿$MR = 160-5L$﻿

﻿$MPMR - 5(160-5L) = 800-25L$﻿

﻿$MPMR = W \rightarrow 800-25L = W$﻿

﻿$LS =\frac {8--}{25}-\frac{1}{25}w$﻿

#### 4 Firms

﻿$MP=10-0.2L$﻿ ﻿$P=10$﻿

﻿$pMP = 100-2L$﻿

﻿$pMP = w \rightarrow 100-2L=w$﻿

﻿$L_2 =50 - \frac{1}{2} w$﻿

﻿$L_3 =50 - \frac{1}{2} w$﻿

﻿$L_4=50 - \frac{1}{2} w$﻿

﻿$L_1=50 - \frac{1}{2} w$﻿

#### Wage Discrimination

Monopolist ﻿$D=1600-8P$﻿ Full Time ﻿$LF =2wF-100$﻿

﻿$Q = 2L$﻿ ﻿$LP=2wP-60$﻿

﻿$P=200 - \frac{1}{8} Q$﻿ ﻿$MR=200 -\frac{1}{4} Q$﻿ ﻿$MRMP = 400 - L$﻿

﻿$=200 -\frac{1}{4} (2L)$﻿

﻿$=200 -\frac{1}{2} L$﻿

﻿$L_f = 2wf -100$﻿ ﻿$w=40 - \frac{1}{4}L$﻿

﻿$L_p = 2wp - 60$﻿ ﻿$\mu c = 40 - \frac{1}{2}L$﻿

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

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

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

USA: ﻿$L=W - 60$﻿ ﻿$Q = \frac{1}{10}L$﻿ ﻿$P=1800-100Q$﻿

CAN: ﻿$L=W - 40$﻿ ﻿$Q = \frac{1}{10}L$﻿ ﻿$P=1200-100Q$﻿

#### Case 1

USA: ﻿$pMP = 180 -10( \frac{1}{10}L)- 180 - L$﻿

﻿$W = L+60$﻿

﻿$180-L=L+60$﻿

﻿$120=2L$﻿

﻿$L=20, \ W=120$﻿

CAN: ﻿$pMP = 120 -10( \frac{1}{10}L)- 120 - L$﻿

﻿$W = L+40$﻿

﻿$120-L=L+40$﻿

﻿$80=2L$﻿

﻿$L=40, \ W=80$﻿

﻿$L^S ?$﻿ ﻿$2W-100 \rightarrow W=50 + \frac{1}{2}L$﻿

﻿$L^S = 50 + \frac{1}{2}L=W$﻿

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

﻿$300-2W$﻿

﻿$L^S = L^P = W=100$﻿

﻿$L_{CAN}=20$﻿﻿$,$﻿ ﻿$L_{USA}=80$﻿

﻿$Q_{USA}= \frac{1}{10} L = 8$﻿ ﻿$Q_{CAN}= \frac{1}{10} L = 2$﻿

﻿$P_{USA} = 1000$﻿ ﻿$P_{CAN} =1000$﻿

"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.