Productivity, Output, and Employment Jeffrey H. Nilsen
Dec 24, 2015
Productivity, Output, andEmployment
Jeffrey H. Nilsen
Asset Market Ch. 7
Growth Ch. 6
Business Cycles Ch. 8
IS-LM, AD-AS Ch. 9 Classics (RBC) Ch. 10 Keynesians Ch. 11 Open Economy Ch. 13
Inflation and Unemployment Ch. 12
Goods Market Ch. 4, Open 5
Labor Market Ch. 3
Monetary Policy Ch. 14
Fiscal Policy Ch. 15
Measurement Ch. 2
http://video.ft.com/2930321275001/Carmakings-centre-of-gravity-moves-east/Companies
Car Production(think of a macro production function?)
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)
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 Function
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)
=
Short-run production
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
Production FunctionCalculating MP without Calculus
Extra question: using calculusFind derivative wrt N and its value at K = 25 and N = 100 ?
=
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
Total Factor Productivity
Y = A F(K, N)
8
3.1 The US Production Function
N DEMAND: Firms can more easily change N (e.g. lay-offs) 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
The Labor Market:Labor Demand
NGroomed
Dogs
MP
0 0 -1 11 112 20 93 27 7
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 = $10 per
grooming
w = 8 groomings per day
𝒘=𝑾 /𝑑𝑎𝑦𝑃 /𝑔𝑟𝑜𝑜𝑚
MP decreases: hiring more workers reduces the new output the next provides
w is given to firm (w won’t change no matter how many workers it hires (thus horizontal line at 8)
For N < N*, if firm hires next worker its profits will increase
Labor demand: for different w, how many workers will the firm hire? We see the MP curve gives the
amount of workers to hire, so it’s ND curve
MP and Labor Demand Graphical Approach
If w rises NO SHIFT; N sinks along fixed ND curve
ND shifts if TFP shock or K rise: higher TFP => workers more productive (those laid off find other jobs)
Aggregate ND: sum of all firms’ ND => same factors affect as in individual firm ND
ND Shifts
Individual (taking w as given) asks: Should I work? She compares Benefit (w) e.g. (Nominal wage (12$))/((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
Labor vs. Leisure Choice
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
NS Upsloping
Fig 3.10 Hours and real per-capita GDP in 36 countries
NS shifts IN if rise in wealth or expected future w (afford more leisure)
NS shifts OUT if rise in population or participation
NS Shifts
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)
Labor Market Eqbm
),( 0 FEFE NKAFY
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
Temporary Productivity (TFP)Shock
A F(K, N*) drops
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
Unemployment in Classic & Keynesian Models
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
Not in LF
9.4 million
Unemployed
2.8 million
5.5%
21%
15.2%
34% 4%
3.7%
LF
Employed
25.4 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
rateU.cyc
*)(2
Yfromdrop Y%
l
UUY
YY
FE
FE
FE
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