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Chapter 3
Productivity, Output, and Employment
生產力，產出與就業
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Abel/Bernanke • Macroeconomics, Fifth Edition
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Learning Objectives
I. Goals of Part 2: The Macroeconomics of Full Employment
A) Analyze factors that affect the longer-term performance of the
economy
B) Develop a theoretical model of the macroeconomy
1. Three markets
a. Labor market (this chapter)
b. Goods market (Ch. 4)
c. Asset market (Ch. 7)
II. Goals of Chapter 3
A) Introduce the production function as the main determinant of
output
1. Discuss the marginal productivity of labor and capital
2. Analyze supply shocks
B) Discuss the determinants of labor demand and supply
C) Equilibrium in the classical model of the labor market
1. Full-employment output
2. Factors that change equilibrium
D) Unemployment
1. Definitions of employment status
2. Frictional, structural, cyclical unemployment
3. Okun’s Law
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Teaching Notes
什麼是函數 Function?
I. How Much Does the Economy Produce?
The Production Function (Sec. 3.1)
Chapter 3 Productivity, Output, and Employment
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生產函數說明產出和投入要素之間的數量關係
給定要素投入量，在現有技術水準下，所可能生產出的最高產量
(在最有效率的情況下)
2 個重點決定此一關係：技術與效率
A) Factors of production
1. Capital 資本財
2. Labor 勞動力
3. Others (raw materials, land, energy)
4. Productivity of factors depends on technology and management
B) The production function
1. Y  AF(K, N)
2. Parameter A is “total factor productivity”
在 K, N 用量不變的情況下，只要 A 變大,產出就會增加
A 的增加代表技術的進步
C) Application: The production function of the U.S. economy and
U.S. productivity growth
1. Cobb-Douglas production function works well for U.S.
economy:
Y  A K 0.3 N 0.7
2. Data for U.S. economy—Table 3.1
3. Productivity growth calculated using production function
a. Productivity moves sharply from year to year
b. Productivity grew slowly in the 1980s and the first half of the
1990s, but increased in the second half of the 1990s
D) The shape of the production function
生產函數圖形上的 2 個特色
(通常產出 y 放在縱軸，要素投入放在橫軸)
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Abel/Bernanke • Macroeconomics, Fifth Edition
1. Two main properties of production functions
a. Slopes upward: 正斜率 more of any input produces more
output
b. Slope becomes flatter as input rises: 斜率遞減
diminishing marginal product as input increases
代表要素投入的邊際產出遞減
2. Graph production function (Y vs. one input; hold other input
and A fixed)
a. Marginal product of capital , MPK 資本財的邊際產出
當資本財增加( K )了一個單位時，產出增加( Y )MPK
個單位
MPK  Y/K
(Figure 3.1; Key Diagram 1; like text Figure 3.2)
Figure 3.1
資本財的邊際產出的特色：
(1) Equal to slope of production function graph (Y vs. K)
資本財的邊際產出即生產函數的斜率
(2) MPK always positive 恆為正
(3) Diminishing marginal productivity of capital
隨資本財數量增加而減少：邊際產出遞減
b. Marginal product of labor, MPN 勞動的邊際產出
Chapter 3 Productivity, Output, and Employment
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當勞動投入增加了一個單位( N )時，產出增加 MPN 個
單位( Y )
MPN  Y/N (Figure 3.2; like text Figure 3.3)
Figure 3.2
勞動的邊際產出的特色：
(1) Equal to slope of production function graph (Y vs. N)
即生產函數的斜率
(2) MPN always positive 恆為正
(3) Diminishing marginal productivity of labor
隨勞動投入增加而減少：邊際產出遞減
E) Supply shocks 供給面的變動 = 生產函數改變
1. Supply shocks affect the amount of output that can be produced
for a given amount of inputs
一些事件(除了要素投入量改變以外)，改變了產出和要素
投入之間的關係
2. Shocks may be positive (increasing output) or negative
(decreasing output) 衝擊有好有壞
3. Examples: weather, inventions and innovations, government
regulations, oil prices
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Abel/Bernanke • Macroeconomics, Fifth Edition
4. Supply shocks shift graph of production function (Figure 3.3;
like text Figure 3.4) 衝擊改變生產函數的圖形
Figure 3.3
a. Negative (adverse) shock: Usually slope of production
function decreases at each level of input (for example, if
shock causes parameter A to decline) 例如 A 變小
b. Positive shock: Usually slope of production function
increases at each level of output (for example, if parameter A
increases)例如 A 變大
II. The Demand for Labor (Sec. 3.2) 勞動需求
相對資本投入，勞動投入可以在短時間內有較大的變動。
就業決定於勞動市場均衡
A) How much labor do firms want to use? 勞動雇用量的決定
由廠商決定勞動需求
1. Assumptions 假設
a. Hold capital stock fixed—short-run analysis
短期資本財數量固定不變(短期的定義)
b. Workers are all alike 所有勞工相同
c. Labor market is competitive 勞動市場完全競爭
廠商是工資的價格接受者
d. Firms maximize profits 廠商追求利潤極大
Chapter 3 Productivity, Output, and Employment
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邊際法則
※最適勞工僱用量決定於 MRPN = W
(廠商會一直增加勞動雇用量直到)
多雇一單位勞動力帶來的好處 =多雇一單位勞動力的成本(W)
多雇一單位勞動力帶來的好處 MRPN
勞動邊際產值 marginal revenue product of labor＝ MPN × P
多雇一單位勞動力的成本
名目工資 W
最適僱用量的決定：
若 MRPN ＞W ＝＞多僱用勞工
若 MRPN ＜W ＝＞少僱用勞工
一直增加僱用量，直到發生
多雇一單位勞動力帶來的好處 ＜多雇一單位勞動力的成本
之前
2. Analysis at the margin: costs and benefits of hiring one extra
worker (Figure 3.4; like text
Figure 3.5)
Figure 3.4
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Abel/Bernanke • Macroeconomics, Fifth Edition
a. If real wage (w)  marginal product of labor (MPN), the firm
is paying the marginal worker more than the worker
produces, so the firm should reduce the number of workers to
increase profits
b. If w  MPN, the marginal worker produces more than he or
she is being paid, so the firm should increase the number of
workers to increase profits
c. Firms’ profits are highest when w  MPN
廠商的利潤極大雇用條件，最適勞動雇用量決定於條件
B) The marginal product of labor and labor demand:
勞動需求線說明勞動雇用量與實質工資之間的關係
an example
The Clip Joint Table 3.2 例如
(1) N
0
1
2
3
4
5
(2) Y
0
11
20
27
32
35
(3) MPN
11
9
7
5
3
(4)MRPN P=$10
$110
$90
$70
$50
$30
1. Example: The Clip Joint—setting the nominal wage equal to
the marginal revenue product of labor (MRPN  P  MPN)
2. W  MRPN is the same condition as w  MPN, since W  P  w
and MRPN  P  MPN
3. A change in the wage
a. Begin at equilibrium where W  MRPN
b. A rise in the wage rate means W  MRPN, unless N is
reduced so the MRPN rises
c. A decline in the wage rate means W  MRPN, unless N rises
so the MRPN falls
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C) The marginal product of labor and the labor demand curve
1. Labor demand curve shows relationship between the real wage
rate and the quantity of labor demanded
2. It is the same as the MPN curve, since w  MPN at equilibrium
3. So the labor demand curve is downward sloping; firms want to
hire less labor, the higher the real wage
D) Factors that shift the labor demand curve
1. Note: A change in the wage causes a movement along the labor
demand curve, not a shift of the curve
2. Supply shocks: Beneficial supply shock raises MPN, so shifts
labor demand curve to the right; opposite for adverse supply
shock
3. Size of capital stock: Higher capital stock raises MPN, so shifts
labor demand curve to the right; opposite for lower capital stock
E) Aggregate labor demand (Figure 3.5)總勞動需求線是單一廠商
勞動需求線的水平加總
Figure 3.5
1. Aggregate labor demand is the sum of all firms’ labor demand
2. Same factors (supply shocks, size of capital stock) that shift
firms’ labor demand cause shifts in aggregate labor demand
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Abel/Bernanke • Macroeconomics, Fifth Edition
III. The Supply of Labor (Sec. 3.3)勞動供給
由個人決定，在「消費商品」與「休閑」之間取捨
A) Supply of labor is determined by individuals
1. Aggregate supply of labor is sum of individuals’ labor supply
2. Labor supply of individuals depends on labor-leisure choice
B) The income-leisure trade-off
1. Utility depends on consumption and leisure
最適工時決定於：個人多工作一小時所得恰能彌補少了一小
時休閒的損失
多工作的好處： 賺 w＝＞可以增加消費＝＞有效用增加
多工作的損失： 少休閒＝＞有效用損失
2. Need to compare costs and benefits of working another day
a. Costs: Loss of leisure time
b. Benefits: More consumption, since income is higher
3. If benefits of working another day exceed costs, work another
day
4. Keep working additional days until benefits equal costs
C) Real wages and labor supply 所得與休閒之間的取捨，比較效
用的增減
1. An increase in the real wage has offsetting income and
substitution effects 當實質工資增加時，效果有二
a. Substitution effect of a higher real wage:
替代效果＝＞因為工作可換得的好處增加了
＝＞增加工時
Higher real wage encourages work, since the reward for
working is higher
b. Income effect of a higher real wage:
所得效果＝＞因為在原工時下，所得提高了
＝＞多消費「休閒」
＝＞減少工時
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Higher real wage increases income for the same amount of
work time, and with higher income, the person can afford
more leisure, so will supply less labor
2. A pure substitution effect: 純替代效果(例)
a one-day rise in the real wage
A temporary real wage increase has just a pure substitution
effect, since the effect on wealth is negligible
3. A pure income effect: 純所得效果(例)
winning the lottery
a. Winning the lottery doesn’t have a substitution effect,
because it doesn’t affect the reward for working
b. But winning the lottery makes a person wealthier, so a person
will both consume more goods and take more leisure; this is
a pure income effect
4. The substitution effect and the income effect together:
實際上的選擇結果如何？視實質工資增加的持續時間而
定。加薪的持續時間越長，所得效果越大。
a long-term increase in the real wage
a. The reward to working is greater: a substitution effect toward
more work
b. But with a higher wage, a person doesn’t need to work as
much: an income effect toward less work
c. The longer the high wage is expected to last, the stronger the
income effect; thus labor supply will increase by less or
decrease by more than for a temporary reduction in the real
wage
5. Empirical evidence on real wages and labor supply 結論
a. Overall result: Labor supply increases with a temporary rise
in the real wage＝＞則(current wage)目前工資 與勞動供給
正相關(假定未來工資不變)＝＞NS 正斜率
b. Labor supply falls with a permanent increase in the real wage
＝＞當工資永久性增加時則勞動供給減少
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Abel/Bernanke • Macroeconomics, Fifth Edition
D) The labor supply curve (Figure 3.6; like text Figure 3.7)假定未來
工資不變，目前實質工資(current real wage)與勞動供給正相關
Figure 3.6
1. Increase in the current real wage should raise quantity of labor
supplied
2. Labor supply curve relates quantity of labor supplied to real
wage
3. Labor supply curve slopes upward because higher wage
encourages people to work more
E) Factors that shift the labor supply curve 改變勞動供給線位置的
外生因素(SUMMARY 4)
1. Wealth 財富: Higher wealth reduces labor supply (shifts labor
supply curve to the left)(－)
2. Expected future real wage 預期未來實質工資改變: Higher
expected future real wage is like an increase in wealth, so
reduces labor supply (shifts labor supply curve to the left)(－)
3.working-age population 成年人口數 (＋)
4.participation rate 勞動參與率(＋)
Chapter 3 Productivity, Output, and Employment
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F) Aggregate labor supply 總勞動供給
1. Aggregate labor supply rises when current real wage rises
a. Some people work more hours
b. Other people enter labor force
c. Result: Aggregate labor supply curve slopes upward
2. Factors increasing labor supply
a. Decrease in wealth
b. Decrease in expected future real wage
c. Increase in working-age population (higher birth rate,
immigration)
d. Increase in labor force participation (increased female labor
participation, elimination of mandatory retirement)
G) Application: weekly hours of work and the wealth of nations
1. In 1869 the average workweek in manufacturing was 56 hours;
it’s now about 40
2. The main reason for the decline is a permanent increase in the
real wage, due to technological innovation and increased
productivity
3. Although the workweek has been about 40 hours since the end
of World War II, lifetime labor supply has declined as workers
now retire earlier and take more vacation time
4. Looking across countries, those with higher real GDP per capita
tend to have lower average workweeks than those with lower
real GDP per capita
5. These results are all consistent with the income effect
dominating the substitution effect for a permanent increase in
the real wage
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Abel/Bernanke • Macroeconomics, Fifth Edition
IV. Labor Market Equilibrium (Sec. 3.4)勞動市場均衡
假定工資無僵固性，隨時可調
A. Equilibrium: Labor supply equals labor demand (Figure 3.7; Key
Diagram 2; like text
Figure 3.11)
Figure 3.7
ND 與 NS 的交點是充份就業狀態
N 充分就業之就業水準， w 充分就業之工資水準
1. Classical model of the labor market—real wage adjusts quickly
2. Determines full-employment level of employment N and
market-clearing real wage w
3. Factors that shift labor supply or labor demand affect N and w
4. Problem with classical model: can’t study unemployment
B) Full-employment output Y 充分就業之產出水準
1. Y  AF(K, N )
2. Y affected by changes in N or production function (example:
supply shock)
Chapter 3 Productivity, Output, and Employment
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C) Application: output, employment, and the real wage during oil
price shocks
1. Sharp oil price increases in 1973–74, 1979–80, 1990
2. Adverse supply shock—lowers labor demand, employment, the
real wage, and the full-employment level of output
3. All three cases: U.S. economy entered recessions
D) Application: technical change and wage inequality
1. Two important features of U.S. real wages since 1970
a. Slowdown in growth of real wages
b. Increased wage inequality
2. Slowdown in productivity growth combined with increased
labor force participation has kept real wages from rising as
much as they did before 1970
3. Skill-biased technical change (such as computerization) has
increased real wages of highly educated workers, but reduced
real wages of unskilled workers (shown graphically)
V. Unemployment (Sec. 3.5) 失業
A) Measuring unemployment 失業的衡量
1. Categories: 根據 BLS 的分類，年滿 16 歲以上的公民(Adult
Population 成年人口)必歸為以下三類之ㄧ
Employed 就業中,過去一週中，有全職、兼差之工作經驗
Unemployed 失業中, 過去一週中未工作，且曾在過去四週中
找工作
not in the labor force 不屬勞動力 過去一週中未工作，且未曾
在過去四週中找工作
2. Labor Force 勞動人口
 Employed 就業人口 Unemployed 失業人口
3. Unemployment Rate 失業率  Unemployed/Labor Force
4. Participation Rate 勞動參與率 Labor Force/Adult Population
5. Employment Ratio 就業率 Employed/Adult Population
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Abel/Bernanke • Macroeconomics, Fifth Edition
Table 3.4 Employment Status of the U.S. Adult Population, 2.2003
Employed workers
137.4(million)
Unemployed workers
8.5
Labor force
Not in labor force
74.3
Adult population
220.2
B) Changes in employment status
1. Flows between categories
C) How long are people unemployed? 失業時間
失業狀況的特色：
1. Most unemployment spells are of short duration
多數的失業期(unemployment spells)持續時間不長，約是 2
個月以內
a. Unemployment spell 失業期 period of time an individual is
continuously unemployed
任何一人處於連續失業狀態 = 處於失業期
b. Duration  length of unemployment spell
2. Most unemployed people on a given date are experiencing
unemployment spells of long duration
在某一天處於失業狀態的人中，多數有長的失業期
3. Reconciling 1 and 2—numerical example:
a. Labor force  100; on the first day of every month, two
workers become unemployed for one month each; on the first
day of every year, four workers become unemployed for one
year each
b. Result: 28 spells of unemployment during year; 24 short (one
month), four long (one year); so most spells are short
Chapter 3 Productivity, Output, and Employment
41
c. At any date, unemployment  six; four have long spells (one
year), two have short spells (one month); so most
unemployed people on a given date have long spells
D) Why there are always unemployed people
為何失業人口永遠不是 0？
1. Frictional unemployment 摩擦性失業
a. Search activity of firms and workers due to heterogeneity
b. Matching process takes time
因為勞工尋找合適的工作；雇主尋找合適的勞工所造成的
失業(配對問題)
2. Structural unemployment 結構性失業
a. Long-term, chronic unemployment 通常是延續性失業、持
續性失業，即使偶有就業也會很快失業(非配對問題)
發生結構性失業的原因：
b. One cause: Lack of skills prevents some workers from
finding long-term employment
技術水準低的勞工
c. Another cause: Reallocation of workers out of shrinking
industries or depressed regions; matching takes a long time
勞工更換就業產業，需要很長的配對、訓練時間
3. The natural rate of unemployment 自然失業率
即使在充份就業狀態仍存在的失業(包括摩擦性失業與結構
性失業)
a. u  natural rate of unemployment; when output and
employment are at full-employment levels
b. u  frictional  structural unemployment
c. Cyclical unemployment:循環性失業
difference between actual unemployment rate and natural rate
of unemployment (u – u )
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Abel/Bernanke • Macroeconomics, Fifth Edition
4. In touch with the macroeconomy: labor market data
a. BLS employment report
(1) Household survey: unemployment, employment
(2) Establishment survey: jobs
VI. Relating Output and Unemployment: Okun’s Law (Sec. 3.6)產出
與失業間的關係
A) Relationship between output (relative to full-employment output)
and cyclical unemployment
B) ( Y – Y)/ Y  2 (u – u )
(3.5
)
循環性失業率每增加 1%，產出與充分就業產出水準之間的差異
就拉大 2%
C) Why is the Okun’s Law coefficient 2, and not 1?
1. Other things happen when cyclical unemployment rises: Labor
force falls, hours of work per worker decline, average
productivity of labor declines
2. Result is 2% reduction in output associated with 1 percentage
point increase in unemployment rate
D) Alternative formulation:


Y/Y  3 – 2 u
(3.6)
Additional Issues for Classroom Discussion
1. Is the Unemployment Rate a Good Measure of Economic
Distress?
2. What Else Is Important for Production?
3. As Your Wage Rises, Do You Supply More Labor? Or
Less?
Chapter 3 Productivity, Output, and Employment
43
4. Why Do Oil Price Shocks Hurt the Economy So Much?
5. Should the Minimum Wage Be Increased?
As a discussion point, you might wish to talk about comparing the
nominal minimum wage to the real minimum wage. Since Congress must
vote to change the nominal minimum wage, it has tended to rise in spurts
over time. Most recently, the minimum wage had been $4.25 per hour
from 1991 to 1996, then went up to $4.75 in 1996 and to $5.15 in 1997.
But, after accounting for inflation, we can see that the real minimum
wage hasn’t kept pace since 1968. Here’s a short history of the nominal
and real minimum wages (deflated by the CPI):
Year 1950 1961 1968 1974 1980 1990 1997 1999 2002
Nominal$0.75 $1.15 $1.60 $2.00 $3.10 $3.80 $5.15 $5.15 $5.15
Real $3.11 $3.85 $4.60 $4.06 $3.76 $2.91 $3.20 $3.09 $2.86
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Abel/Bernanke • Macroeconomics, Fifth Edition