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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.
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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