Labor econ

1. Seminar 11-Revision
Associate Professor Deniz Guvercin

2. Exam Preview
• Number of Questions: 8
• Number of Quantitative Questions: 2
• Marks Share of Quantitative Questions: 30 %
• Seminars to Prepare Quantitative Questions: Seminar 4,Seminar 5,
Seminar 6, Revision Seminar.
• To Prepare Essay Type of Questions: Read Borjas. Read Lecture Notes.
Chapters: Chapter 5 (Minimum Wage), Labor Market Equilibrium, Wage
Structure, Migration, Discrimination, Human Capital.

3. Labor Market Equilibrium, Minimum Wage & Payroll Tax.
• Suppose that the Utility function for the people in the society and production
function for the firms in the economy is the following :
𝑈 𝑐 = 𝑙𝑜𝑔(𝑐)
𝐹 𝐿 = 10𝐿 − 𝐿2
Suppose that number of firms in the economy is 1 and also number of people in the
society are 1. Price for the consumption good is 1.
• Find the labor market equilibrium?
• Suppose that government introduces minimum wage policy where it sets the
minimum wage to 1$ more of the market wage. Find the employment level? Find
the deadweight loss?
• Suppose that the government taxes the employers by 1$ per hour? Find the new
wage level? Find distribution of total surpluses? Is there any deadweight loss?

4. Answer
• 𝐿𝑆
= 1
• 10 − 2𝐿 = 𝑊 ⇒ 𝐿𝐷 =
10−𝑊
2
• Equilibrium wage:
10−𝑊
2
= 1 ⇒ 𝑊 = 8
After minimum wage policy: 𝑊 = 9
New employment Level is 𝐿𝐷 =
10−9
2
=
1
2
Unemployment: 1 −
1
2
=
1
2

5. Answer
• Deadweight loss: It is the surplus that exists but can’t be captured due to
market interventions.
• 10 − 2𝐿 is the VMP below it, there is some to be shared. However, we have
inelastic labor supply curve, so that there is no (opportunity) cost of market
attendance. Therefore the deadweight loss is the following:
Deadweight Loss : 1
2
1
(10 − 2𝐿)𝑑𝐿 = 4.25

6. Answer
• When there is 1$ tax on employers:
• 10 − 2𝐿 = 𝑊 + 1 defines new labor demand.( Right hand side is cost
of labor, left hand side is VMP.)
• 𝐿𝐷
=
9−𝑊
2
• Solving for equilibrium:
• 𝑊 = 7
• Total Output: 0
1
(10 − 2𝐿)𝑑𝐿 = 9

7. Answer
Distribution Before Tax:
• Wage : 8 – Worker’s Surplus
• Tax: 0$
• Profit: 1$
Distribution After Tax:
• Wage : 7 – Worker’s Surplus
• Tax: 1$
• Profit: 1$
• There is no deadweight loss.

8. Labor Market Equilibrium, Factor Employment&Unemployment
• Suppose that Labor is supplied inelastically and the production function for
the firms is the following:
𝐹 𝐾, 𝐿 = 𝑀𝑖𝑛{𝐿, 𝐾}
Find the labor demand function?
Find the equilibrium wage given that equilibrium rental price of capital is 𝑟?
Suppose that the production function is the following:
𝐹 𝐾, 𝐿 = 𝑀𝑖𝑛 𝐴𝐿, 𝐾
Find the new equilibrium wage level given that equilibrium rental price of
capital is 𝑟?

9. Answer
As we discussed before profit maximization requires
𝐿∗
= 𝑄 = 𝐾∗
Profit maximization also requires for 𝑄 > 0:
𝑃𝑄 − 𝑤𝑄 − 𝑟𝑄 ≥ 0 ⇒ Q P − w + r ≥ 0
Therefore: If P − w + r < 0 then 𝐿∗ = 0 = 𝐾∗.
If P − w + r ≥ 0 , then 𝑄 ≥ 0 so that 𝐿∗≥ 0
On the other hand if P − w + r > 0 there is no maximand 𝐿∗
while
P − w + r = 0 𝐿∗
is horizontal. Therefore for inelastically supplied labor.
Employment is 𝐿 and equilibrium wage is P − r for given r.
(In the long run there is no profit)

10. Answer
• After production function change we have following demand functions:
𝐿∗
=
𝑄
𝐴
, 𝑄 = 𝐾∗
Profit function becomes:
𝑃𝑄 − 𝑤
𝑄
𝐴
− 𝑟𝑄 ≥ 0 ⇒
𝑄
𝐴
A P − 𝑟 − 𝑤 ≥ 0
Employment is 𝐿 and equilibrium wage is A(P − r)
(In the long run there is no profit)

11. Labor Market Equilibrium, Factor Employment&Unemployment
• Suppose that Labor and Capital (such as buildings) are supplied inelastically
(𝐿, 𝐾) and the production function for the firms is the following:
𝐹 𝐾, 𝐿 = 𝐾 + 𝐿
Find the labor and capital demand functions?
Find the equilibrium wage and rental price of capital?
Find the unemployment condition in the labor market?

12. Answer
Profit maximization requires for 𝐹 𝐾, 𝐿 = 𝐾 + 𝐿 ∶
𝑤 = 𝑟 𝑓𝑜𝑟 𝐾 > 0 𝑎𝑛𝑑 𝐿 > 0 𝑖𝑓𝑓 𝑃 ≥ 𝑤 or 𝑃 ≥ 𝑟
By profit maximization:
If 𝑤 > 𝑟 , only 𝐾 is used. 𝐾∗ = 𝑄 𝑖𝑓𝑓 𝑃 ≥ 𝑟
If r > 𝑤 only 𝐿 is used. 𝐿∗ = 𝑄. 𝑖𝑓𝑓 𝑃 ≥ 𝑤.

13. Answer
• Labor Demand Function:
• 𝑃 > 𝑤 𝑎𝑛𝑑 𝑤 < 𝑟: 𝐿∗ 𝑖𝑠 𝑛𝑜𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑
• 𝑃 < 𝑤 𝑎𝑛𝑑 𝑤 < 𝑟: 𝐿∗ = 0
• 𝑃 = 𝑤 𝑎𝑛𝑑 𝑤 < 𝑟: 𝐿∗
≥ 0.
• Capital Demand Function:
• 𝑃 > 𝑟 𝑎𝑛𝑑 𝑟 < w: 𝐾∗
𝑖𝑠 𝑛𝑜𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑
• 𝑃 < 𝑟 𝑎𝑛𝑑 𝑟 < w: 𝐾∗ = 0
• 𝑃 = 𝑟 𝑎𝑛𝑑 𝑟 < w: 𝐾∗
≥ 0.

14. Answer
• There is no unemployment in any factor market:
𝑄 = 𝐿 + 𝐾
If there is no unemployment
𝑟 = 𝑤
In the long run there is no profit so that :
𝑟 = 𝑤 = 𝑃

15. Answer
• If there is unemployment in the labor market:
𝑃 ≥ 𝑟 𝑎𝑛𝑑 𝑤 > 𝑟: 𝐿∗ = 0 and 𝑄 = 𝐾
• If there is unemployment in the capital market:
𝑃 ≥ 𝑤 𝑎𝑛𝑑 𝑟 > w: 𝐾∗ = 0 and 𝑄 = 𝐿

16. Labor Mobilization
• Suppose that the following production function is the following valid in
both regions 𝐴, 𝐵:
𝐹 𝐿 = 10𝐿 − 𝐿2
• Suppose that the labor is inelastically supplied in both regions. In
region A labor supplied inelastically is 0.25, while in the region B it is
0.75.
• Find the equilibrium wage before labor mobilization?
• Find the equilibrium wage and employment after labor mobilization?
• Compare outputs before and after mobilization?

17. Answer
• 10 − 2𝐿 = 𝑊 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚: 10 − 2(0.25) = 𝑤𝑎 = 9.5
• 10 − 2𝐿 = 𝑊 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚: 10 − 2 0.75 = 𝑤𝑏 = 8.5
• Total Output:
• 𝑄𝑎 = 10 0.25 − 0.25 2 = 2,4375
• 𝑄𝑏 = 10 0.75 − 0.75 2
= 6,9375
• 𝑄𝑎 + 𝑄𝑏 = 9,375

18. Answer
• 10 − 2𝐿 = 𝑊 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚: 10 − 2(0.25 + 𝑥) = 𝑤 x
• 10 − 2𝐿 = 𝑊 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚: 10 − 2 0.75 − 𝑥 = 𝑤
• 10 − 2(0.25 + 𝑥) = 10 − 2 0.75 − 𝑥 ⇒ 𝑥 = 0.25
• Total Output:
• 𝑄𝑎 = 10 0.5 − 0.5 2 = 4,75
• 𝑄𝑏 = 10 0.5 − 0.5 2 = 4,75
• 𝑄𝑎 + 𝑄𝑏 = 9,5

19. Monopsony
Suppose that there is only one firm participating to labor market and renting
the labor. The firm has following labor demand curve: 10 − 2𝐿𝐷 = 𝑤. The
labor supply in the market can be defined as follows: 4 + 𝐿𝑆 = 𝑤.
• Find the competitive profit level?
• Find the profit obtained by the perfectly discriminating monopsony?
• Find the profit obtained by the perfectly non-discriminating monopsony?

20. Answer
• Competitive Wage:
10 − 2𝐿∗
= 𝑤∗
= 4 + 𝐿∗
⇒ 𝐿∗
= 2, 𝑤∗
= 6
• Competitive Profit:
0
𝐿∗
(𝑉𝑀𝑃(𝐿) − 𝑤∗)dL =
0
2
10 − 2𝐿 − 6 𝑑𝐿 = 4
• Monopsony Profit:
0
𝐿∗
(𝑉𝑀𝑃 𝐿 − 𝑊( 𝐿𝑆
))dL =
0
2
10 − 2𝐿 − 4 − 𝐿 𝑑𝐿 = 6
𝑀𝑜𝑛𝑜𝑝𝑠𝑜𝑛𝑦 𝑃𝑟𝑜𝑓𝑖𝑡 > 𝐶𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑖𝑣𝑒 𝑃𝑟𝑜𝑓𝑖𝑡

21. Answer
• TFC should be calculated for perfectly non-discriminating case:
• 𝑇𝐹𝐶 = 𝑊𝑎𝑔𝑒 (𝐿𝑆
). 𝐿
• 𝑀𝐹𝐶 =
𝑑𝑇𝐹𝐶
𝑑𝐿
• 𝑊𝑎𝑔𝑒 (𝐿𝑆
) - is wage cost for the perfectly non-discriminating monopsony
derived from labor supply function.
• 4 + 𝐿𝑆
= 𝑤
• 𝑇𝐹𝐶 = 4 + 𝐿 𝐿 = 4𝐿 + 𝐿2
• 𝑀𝐹𝐶 = 4 + 2L
• At equilibrium:
• 𝑉𝑀𝑃 𝐿∗
= 𝑀𝐹𝐶 𝐿∗
• 10 − 2𝐿∗
= 4 + 2𝐿∗
→ 𝐿∗
= 1.5
• 𝑃𝑟𝑜𝑓𝑖𝑡 = 0
1.5
(10 − 2L − 4 − 2L)𝑑𝐿 = 4.5