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