Download Macroeconomic Analysis Econ 6022 Level I

Macroeconomic Analysis
Econ 6022
Level I
Lecture 3
Fall, 2011
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Overview
• The Production Function
• Labor Market
- The Demand for Labor
- The Supply of Labor
- Labor Market Equilibrium
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The Production Function
• Roughly speaking, goods and services produced by the
economy is GDP.
• How do we describe this production process?
• It is rather complicated ...
• Simplification: One goods economy!
• Factors of production
-
Capital (K)
Labor (N)
Others (raw materials, land, energy)
Productivity of factors depends on technology and
management
• Production function: relationship between input (production
factors) and output
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The Production Function
• The production function
Y = A · F (K , N)
(3.1)
- Parameter A is "total factor productivity" (the effectiveness
with which capital and labor are used)
- Variable N is labor input
- Variable K is capital
• We define as capital the tools needed for production, i.e.,
the physical objects that extend our ability or do work for
us.
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Five features of capital:
1. It is productive: it raises the amount of output that a
worker can produce.
2. It is produced: Capital has itself been produced through
the process of investment (private or public).
3. It is rival in its use: only a limited number of people can
use a given piece of capital at one time.
4. It yields a return: Since it makes a worker more
productive, the worker or its firm will be willing to pay (the
owner) to use it.
5. It wears out: Using capital causes it to wear down a little,
which is called depreciation.
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The properties of the Production Function
• Two general Properties
- Slopes upward: more of any input produces more output
- Slope becomes flatter as input rises: diminishing marginal
product as input increases
• Show them graphically
- Graph production function
- Output vs. one input
- hold other input and A fixed
• Show them mathmatically
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Figure 3.1 The Production Function Relating Output and
Capital
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Marginal Product of Capital
• Marginal product of capital, MPK = ∆Y /∆K
- Equal to slope of production function graph (Y vs. K)
- MPK always positive
- Diminishing marginal productivity of capital: MPK declines
as K rises
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Figure 3.2 The marginal product of capital
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Marginal Product of Labor
• Marginal product of labor, MPN = ∆Y /∆N
- Equal to slope of production function graph (Y vs. N)
- MPN always positive
- Diminishing marginal product of labor: MPN declines as L
rises
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Figure 3.3 The production function relating output and labor
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The Cobb-Douglas Production Function
• Cobb-Douglas production function is most often used in
macroeconomics.
Y = A · K α N 1−α
• The relationship between input and output in industrial
economies is described reasonably well by Cobb-Douglas
production function.
• The key is to estimate the parameter α
• Data show: α ≈ 0.3
• We could also show theoretically that 0 < α < 1
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Math Representation
• Actually, all the discussion on production function can be
summarized with a few equations.
∂Y
∂Y
- Property 1: MPK =
> 0; MPN =
>0
∂K
∂N
∂MPK
∂MPN
- Property 2:
< 0;
<0
∂K
∂N
• Take Cobb-Douglas production function for example:
- Property 1: MPK = A · α · K α−1 · N 1−α > 0
∂MPK
= A · α · (α − 1) · K α−2 · N 1−α < 0
- Property 2:
∂K
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Constant Returns to Scale
• Additional property of production function
• Def: If we multiply the quantities of each input by some
factor, the quantity of output will increase by the same
factor.
F (zK , zN) = zF (K , N)
• Intuitively, it makes sense: double all the inputs of
production and output doubles
• That’s “the standard replication argument ” .
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Constant Returns to Scale
• It is also useful and often used later on:
• Transform production function in aggregate term to per
worker term
1
1
Y = F (K , N) = F
N
N
...or defining k =
K
N
and y =
K N
,
N N
=F
K
,1
N
Y
N,
rewrite
K
1
Y =F
,1
N
N
• Output per worker is a function only of capital per worker.
y = F (k , 1) = f (k )
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Supply shocks
• We have been discussing about K , N, α and now we turn
to the other element of the production function.
• Supply shocks: change in productivity parameter A
- Supply shock = productivity shock = a change in an
economy’s production function
- Supply shocks affect the amount of output that can be
produced for a given amount of inputs
- Shocks may be positive (increasing output) or negative
(decreasing output)
- Examples: weather, inventions and innovations,
government regulations, oil prices
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Supply shocks
• Show supply shocks graphically
• Supply shocks shift graph of production function (Fig. 3.4)
• Negative (adverse) shock: Usually slope of production
function decreases at each level of input (for example, if
shock causes parameter A to decline)
• Positive shock: Usually slope of production function
increases at each level of output (for example, if parameter
A increases)
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Figure 3.4 An adverse supply shock that lowers the MPN
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Labor Market
• Discussion on labor market is closely linked with
production function. We will see immediately.
• Market for labor v.s. market for ice cream.
• Labor input is demanded by FIRMS.
• Labor input is supplied by INDIVIDUALS.
• Equilibrium wage clears the market.
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The Demand for Labor
• How much labor do firms want to use? Assumptions
- Hold capital stock fixed (short-run analysis)
- Workers are all alike (simplification)
- Labor market is competitive (taking price as given)
- Firms maximize profits (optimization)
• A thought experiment: marginal benefit and cost of hiring
an additional unit of labor (MPN and real wage)
• Analysis at the margin: costs and benefits of hiring one
extra worker (Fig. 3.5)
- If w > MPN, profit rises if number of workers declines
- If w < MPN, profit rises if number of workers increases
- Firms’ profits are highest when w = MPN
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Figure 3.5 The determination of labor demand
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The Demand for Labor
• The marginal product of labor and the labor demand curve
- Labor demand curve shows relationship between the real
wage rate and the quantity of labor demanded
- It is the same as the MPN curve, since w = MPN at
equilibrium
- So the labor demand curve is downward sloping; firms want
to hire less labor, the higher the real wage
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The Demand for Labor
• Factors that shift the labor demand curve
- Note: A change in the wage causes a movement along the
labor demand curve, not a shift of the curve
- Supply shocks: Beneficial supply shock raises MPN, so
shifts labor demand curve to the right; opposite for adverse
supply shock
- Size of capital stock: Higher capital stock raises MPN, so
shifts labor demand curve to the right; opposite for lower
capital stock
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The Demand for Labor
• Aggregate labor demand
- Aggregate labor demand is the sum of all firms’ labor
demand
- Same factors (supply shocks, size of capital stock) that shift
firms’ labor demand cause shifts in aggregate labor
demand
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Figure 3.6 The effect of a beneficial supply shock on labor
demand
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The Supply of Labor
• Supply of labor is determined by individuals
- Aggregate supply of labor is the sum of individuals’ labor
supply
- Labor supply of individuals depends on labor-leisure choice
- Total available time = working time + leisure time
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The Supply of Labor
• The income-leisure trade-off
-
Utility depends on consumption and leisure
U(c, l): c consumption and l leisure time
Price of leisure time relative to consumption good?
Real wage rate, w, and nominal real wage rate , W ,
W
- w=
P
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Real wages and labor supply
• An increase in the real wage has offsetting income and
substitution effects
- Substitution effect: Higher real wage encourages work,
since the price of leisure time is higher
- Income effect: Higher real wage increases income for same
amount of work time, so person can afford more leisure, so
will supply less labor
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The Supply of Labor
• A pure substitution effect: 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
• A pure income effect: winning the lottery
- Winning the lottery doesn’t have a substitution effect,
because it doesn’t affect the reward for working
- 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
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The Supply of Labor
• A long-term increase in the real wage
- The reward to working is greater: a substitution effect
toward more work
- But with higher wage, a person doesn’t need to work as
much: an income effect toward less work
- 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
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The Supply of Labor
• Empirical evidence on real wages and labor supply
- Overall result: Labor supply increases with a temporary rise
in the real wage
- Labor supply falls with a permanent increase in the real
wage
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The Labor Supply Curve
• Increase in the current real wage should raise quantity of
labor supplied?
• YES, NO or It depends?
• Labor supply curve relates quantity of labor supplied to
current real wage by holding other things equal (including
future wage rates).
• Labor supply curve slopes upward because higher current
wage encourages people to work more
• Future wage rate is a curve shifter.
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Figure 3.7 The labor supply curve of an individual worker
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The Supply of Labor
• Factors that shift the labor supply curve
- Wealth: Higher wealth reduces labor supply (shifts labor
supply curve to the left, as in Fig. 3.8)
- Expected future real wage: Higher expected future real
wage is like an increase in wealth, so reduces labor supply
(shifts labor supply curve to the left)
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Figure 3.8 The effect on labor supply of an increase in wealth
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Aggregate labor supply
• Aggregate labor supply rises when current real wage rises
- Some people work more hours
- Other people enter labor force
- Result: Aggregate labor supply curve slopes upward
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Factors increasing labor supply
• Decrease in wealth
• Decrease in expected future real wage
• Increase in working-age population (higher birth rate,
immigration)
• Increase in labor force participation (increased female
labor participation, elimination of mandatory retirement)
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Labor Market Equilibrium
• Labor market equilibrium: Labor supply equals labor
demand
• Equilibrium wage, w
• Equilibrium labor input, N
• How does the labor market respond to shocks?
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Figure 3.10 Labor market equilibrium
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Figure 3.11 Effects of a temporary adverse supply
shock on the labor market
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Labor Market Equilibrium
• Full-employment output
• Full-employment output = potential output = level of output
when labor market is in equilibrium
Ȳ = A · F (K , N̄)
(3.4)
• affected by changes in full employment level or production
function (example: supply shock, Fig. 3.11)
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