Transcript ú m p.fr
Productivity, Output, and
Employment
Jeffrey H. Nilsen
Inflation and Unemployment
Ch. 12
Monetary Policy
Fiscal Policy
Ch. 14
Ch. 15
Business Cycles Ch. 8
IS-LM, AD-AS
Classics (RBC)
Keynesians
Open Economy
Asset Market
Ch. 7
Ch. 9
Ch. 10
Ch. 11
Ch. 13
Labor Market
Ch. 3
Measurement
Ch. 2
Growth
Ch. 6
Goods Market
Ch. 4, Open 5
Car Production
(think of a macro production function?)
http://video.ft.com/2930321275001/Carmakingscentre-of-gravity-moves-east/Companies
Long run Production Function
In long run: firms &
workers can change
both K & N used in
production
Y = A F(K, N)
Y = A K0.5 N0.5 (cobb-douglas)
Short run Production Function
In short-run (business cycle): assume K
fixed => firms’ & workers’ N choices
determine Y
Y = A F(K, N)
Y = A K0.3 N0.7 (cobb-douglas)
Short-run production
𝑆𝑙𝑜𝑝𝑒: 𝑀𝑃𝑁 =
Slope > 0. Next unit N raises output but MP diminishes as N rises
Diminishing MPN (new N unit must share same K with greater
number of others)
∆𝑌
∆𝑁
Production Function
Calculating MP without Calculus
𝑀𝑃𝑁 =
∆𝑌
∆𝑁
Cobb-Douglas example:
Y = A K1/2 N1/2
Let A = 1, K = 25, N = 100
=> Y = 50
Then if N rises to 121
=> Y = 55
So Y rises by 5 from greater labor by 21 => MPN = 5/21 or
ca. ¼… In words, at K=25, N=100, next new worker will
add ¼ unit of output
Extra question: using calculus
Find derivative wrt N and its value at K = 25 and N = 100 ?
Total Factor Productivity
Y = A F(K, N)
Improved “A” or TFP (better “methods” or knowledge)
=> each N or K unit able to produce greater output
Exogenous (assume certain value for variable [its value is
given from outside the model])
Adverse TFP shock: production drops at all N levels =>
production function shifts down
Examples: drought or oil prices (imposes higher input costs
for industries in oil importing nations)
Distinct from Y/N (average labor productivity) which
measures average output over all workers
3.1 The US Production Function
8
The Labor Market:
Labor Demand
N DEMAND: Firms can more easily change N (e.g. layoffs) vs. long-lived K (new K has small effect on total K)
Measure N as time worked or number of employees
Assume:
Workers identical (same level of skills, ambition, etc)
Firms identical & small, each one takes wage as given from
competitive labor market
Firm will hire the next worker so long as the benefit of
hiring her exceeds the costs
Benefit exceeds costs =>
Firm maximizes profits
For the firm:
MPN = benefit of hiring the next
worker
MC, cost of hiring the next worker is
real wage w
Assume nominal W = $80 per day
Output price = $10 per grooming
w = 8 groomings per day
𝒘=
𝑾/𝑑𝑎𝑦
𝑃/𝑔𝑟𝑜𝑜𝑚
N Groomed MP
Dogs
0
0
1
11
11
2
20
9
3
27
7
MP and Labor Demand
Graphical Approach
MP decreases: hiring more workers
reduces the new output the next
provides
w is given to firm (w won’t change
no matter how many workers it hires
(thus horizontal line at 8)
For N < N*, if firm hires next worker
its profits will increase
Labor demand: for different w, how
many workers will the firm hire?
We see the MP curve gives the
amount of workers to hire, so it’s ND
curve
ND Shifts
If w rises NO SHIFT; N sinks along fixed ND curve
ND shifts if TFP shock or K rise: higher TFP => workers
more productive (those laid off find other jobs)
Aggregate ND: sum of all firms’ ND => same factors
affect as in individual firm ND
Labor vs. Leisure Choice
Individual (taking w as given) asks: Should I work? She
compares
Benefit (w) e.g. (Nominal wage (12$))/((3$) avg P of goods
purchased) => she’ll receive 4 units of goods by working
next hour
Her MC: leisure to give up if she works the next hour
NS Upsloping
w rise alters individual’s labor/leisure trade-off:
Long-run (or permanent): income effect dominant (feel
richer, want to enjoy more leisure) => NS falls
Empirical: many nations’ rising long-run productivity (& w) cut
hours worked
Short-run (or temporary): substitution effect dominant
(rising opportunity cost of leisure cuts leisure to work more)
=> NS rises
For model, assume given expected future w (and wealth)
Aggregate NS up-sloping also due to higher w attracting
to join LF
Fig 3.10 Hours and real per-capita
GDP in 36 countries
NS Shifts
NS shifts IN if rise in wealth or expected future w
(afford more leisure)
NS shifts OUT if rise in population or participation
Labor Market Eqbm
Single firm takes w as given, but in market,
w* & N* determined together
Classic model => w adjusts quickly so NS = ND
If w < w*, ND > NS => firms bid up w to hire N
to max profits
At w*, NS = ND, N* is full-employment N
Y* (or YFE) (Full-Employment Y)
corresponds to N* => when W, P fully
adjusted (Y* is economy’s output capacity)
YFE AF ( K 0, NFE )
Temporary Productivity (TFP)
Shock
E.g. Adverse shock in A has 2 effects:
Direct: Y* falls at initial N*
Indirect: MPN drop at N* shifts ND,
new eqbm N**
NS stable: temporary => no change in
expected future w
A F(K, N*) drops
Unemployment in Classic &
Keynesian Models
Classics don’t explain U (anyone wanting to work at
w* gets job => U = 0)
Keynesian U assumes “sticky” wage adjustment
(excess NS)
RBC (new classics) explain U by reasoning it takes
time to match workers to jobs
EU quarterly Labor Force Survey
Person who has worked either full or part time in past
week is “employed”
If she didn’t work in past week, but had looked for
work in past 4 weeks she is “unemployed”
Non-LF person: if didn’t work in past week and didn’t
look for work in past 4 weeks (e.g. student)
U rate = U/(LF) or U/(E + U)
Employment ratio = E/(adult population)
Table 3.4 US Employment Status of Adult
Population, Feb 2003
Fig 3.15 Changes in UK employment status in
typical month
LF
Employed
3.7%
25.4 million
Not in LF
15.2%
9.4 million
34%
4%
5.5%
Unemployed
21%
2.8 million
Unemployment Stylized Fact
Most spells are of short duration, but most of those
unemployed at a given time are suffering spells of long
duration
Spell: period when person continuously unemployed
Duration: the length of time unemployed (indicates degree
of hardship)
Simple explanatory example of 100 people in LF:
Each month 2 workers become unemployed and stay
unemployed for a month (frictional) 24 spells
Each year 4 workers become unemployed and stay
unemployed for year (structural) = 4 spells
On any given day, unemployed consist of 2 short and 4 long.
Natural Rate of Unemployment
Frictional U
Structural U
Cyclical U: (U – U*)
Positive (U high) when Y < Y*
Okun’s law: for each 1% rise in U above natural rate, GDP
drops 2% below YFE
Y YFE
2 (U U *)
YFE
cycl.U rate
% Y drop
from YFE
Fig 3.16 Okun’s law in US
5. One reason that firms hire labor at the point where w = MPN is
(a) if w < MPN, the cost (w) of hiring additional workers exceeds the
benefits (MPN) of hiring them, so they should hire fewer workers.
(b) if w > MPN, the cost (w) of hiring additional workers is less than the
benefits (MPN) of hiring them, so they should hire more workers.
(c) if w < MPN, the cost (w) of hiring additional workers equals the
benefits (MPN) of hiring them, so they have the right number of
workers.
(d) if w > MPN, the cost (w) of hiring additional workers exceeds the
benefits (MPN) of hiring them, so they should hire fewer workers.
The Upstart Company has a production function:
# Workers
# Cases Produced
0
0
1
10
2
19
3
26
4
31
5
34
If Upstart hires 4 workers, which could be the real wage?
(a) 2
(b) 4
(c) 6
(d) 8
Which of these events would lead to an increase in
the MPN for every quantity of labor?
(a) An increase in the real wage
(b) A decrease in the real wage
(c) A favorable supply shock such as a fall in the price
of oil
(d) An adverse supply shock, such as a reduced supply
of raw materials