CONSUMPTION-LABOR FRAMEWORK
(aka CONSUMPTION-LEISURE FRAMEWORK)
CHAPTER 2
2THE THREE MACRO (AGGREGATE) MARKETS
The Road Ahead
 Goods Markets
 Labor Markets
 Financial/Capital/Savings/Asset
Markets
 Will put micro-foundations under all three
c
P
labor
wage
capital
interest
rate
3BASICS
Introduction
 Consumption-Leisure Framework – provides foundation for
 Labor-market supply function
 Goods-market demand function
 An application of the basic consumer theory model…
 …we will put a macro interpretation on it
 Only one time period – no “future” for which to save
 Notation
 c: consumption (“all stuff”)
 n: number of hours spent working per unit
 l: number of hours leisure per unit (time spent not working)
 P: dollar price of one unit of consumption (a nominal variable)
 W: hourly wage rate in terms of dollars (a nominal variable)
 t: tax rate on labor income
 “Weekly,” “monthly,” “yearly” is a detail
 Just need to take SOME stand on the length of a “period”
 n + l = 1  n (l) is the percentage of time working (in leisure)
n + l = 1
4BASICS
Introduction
 Building blocks of consumption-leisure framework
 Utility
 Describes the benefits of engaging in labor market (and other)
activities
 Budget constraint
 Describes the costs of engaging in labor market (and other) activities
 Utility and budgets two DISTINCT concepts
 As in basic consumer analysis (Chapter 1)
 Only after describing utility and budgets separately do we bring
the two together to obtain predictions from the framework
5UTILITY
Model Structure
 Preferences u(c, l) with all the “usual properties”
 Strictly increasing in c
 Strictly increasing in l
 Diminishing marginal utility in c
 Diminishing marginal utility in l
 Plotted in good-by-good spaces:
 Plotted as indifference curves
 Utility side of consumption-leisure
framework identical to Chapter 1
framework
c
u(c,l)
leisure
u(c,l)
leisure
c
6BUDGET CONSTRAINT
Model Structure
 Consumer must work for his income
 Y no longer “falls from the sky”
Pc Y
(1 )Pc t Wn 
Y = (1-t)Wn (all income is after-tax labor income)
Rearrange
1 1 2 2Pc Pc Y 
Spending
on c1
Spending
on c2
A constant from the point
of view of the individual
Simply an application/re-
interpretation of our basic
consumer theory framework
Chapter 1 budget constraint
(After-tax) wage is opportunity cost
of leisure, hence the “price” of leisure
- opportunity costs are real economic
costs/prices
A constant from the
point of view of the
individual (price-
taker)
Spending on
consumption
(1 ) (1 )Pc t Wl t W   
(1 ) (1 )Pc t W l  
n = 1 – l
“Spending”
on leisure
7CONSUMER OPTIMIZATION
Model Structure
 Consumer’s decision problem: maximize utility subject to budget
constraint – bring together both cost side and benefit side
 Choose c and l subject to
 Plot budget line
leisure
c
(1 ) (1 )c t Wl WP t   
Isolate c to
graph the
budget
constraint
) (1 )(1c t W tlP W   
) 1 )(1 (t W
P
t W
c l
P
 



 

slope = -(1-t)W/P
IMPORTANT: the
larger is (1-t)W/P,
the steeper is the
budget line
1
(1 ) (1 )Pc t Wl t W   
8CONSUMER OPTIMIZATION
Model Structure
 Consumer’s decision problem: maximize utility subject to budget
constraint – bring together both cost side and benefit side
 Choose c and l subject to
 Plot budget line
 Superimpose indifference map
 At the optimal choice
leisure
c
slope = -(1-t)W/P
optimal choice (c*,l*)
( *, *) (1 )
( *, *)
l
c
u c l t W
u c l P


CONSUMPTION-LEISURE
OPTIMALITY CONDITION
- A key building block of
modern macro models
MRS (between
consumption
and leisure)
price ratio
(inclusive of
taxes)
IMPORTANT: the
larger is (1-t)W/P,
the steeper is the
budget line
1
(1 ) (1 )Pc t Wl t W   
9REAL WAGE
Macro Fundamentals
 W/P a crucial measure for macroeconomic analysis
 Unit Analysis (i.e., analyze algebraic units of variables)
 Units(W) = $/hour of work
 Units(P) = $/unit of consumption
 Units(W/P) =
 Economic decisions depend on real wages (W/P), not nominal
wages (W)
 Measures the purchasing power of (nominal) wage earnings…
 …which is presumably what people most care about
$
$ unit of consumptionhour of work
$ hour of work $
unit of consumption
unit of consumption
hour of work
 
 Will sometimes denote
using w (lower-case…)
10
CONSUMER OPTIMIZATION
The Graphics of the Consumption-Leisure Model
 Consumer’s decision problem: maximize utility subject to budget
constraint – bring together both cost side and benefit side
 Choose c and l subject to
 Plot budget line
 Superimpose indifference map
 At the optimal choice
leisure
c
slope = -(1-t)W/P
optimal choice (c*,l*)
( *, *) (1 )
( *, *)
l
c
u c l t W
u c l P


CONSUMPTION-LEISURE
OPTIMALITY CONDITION
- key result in modern macro
analysis
MRS (between
consumption
and leisure)
After-tax real
wage
Derive consumption-leisure
optimality condition using
Lagrange analysis
IMPORTANT: the
larger is (1-t)W/P,
the steeper is the
budget line
1
(1 ) (1 )Pc t Wl t W   
11
LAGRANGE ANALYSIS
The Mathematics of the Consumption-Leisure Model
 Apply Lagrange tools to consumption-leisure optimization
 Objective function: u(c,l)
 Constraint: g(c,l) = (1-t)W – Pc – (1-t)Wl = 0
 Step 1: Construct Lagrange function
 Step 2: Compute first-order conditions with respect to c, l, λ
 Step 3: Combine (1) and (2) (with focus on eliminating multiplier)
* *
* *
( , ) (1 )
( , )
l
c
u c l t W
u c l P


CONSUMPTION-LEISURE
OPTIMALITY CONDITION
MRS (between
consumption and leisure)
After-tax real
wage
( , ) 0cu c l P 
( , ) (1 ) 0lu c l t W  
(1 ) (1 ) 0t W Pc t Wl    
 ( , , ) ( , ) (1 ) (1 )L c l u c l t W Pc t Wl      
12
MICRO-LEVEL LABOR SUPPLY
Labor Supply in the Micro
An experiment: how do micro-level consumption/leisure choices
change as the real wage changes (assume t = 0 here for simplicity)
REAL WAGES: (W/P)1 < (W/P)2
leisure
c
slope = -(W/P)1
l*1
c*1
slope = -(W/P)2
l*2
c*2
1
13
MICRO-LEVEL LABOR SUPPLY
Labor Supply in the Micro
An experiment: how do micro-level consumption/leisure choices
change as the real wage changes (assume t = 0 here for simplicity)
REAL WAGES: (W/P)1 < (W/P)2 < (W/P)3
leisure
c
slope = -(W/P)1
l*1
c*1
slope = -(W/P)2
l*2
c*2 slope = -(W/P)3
l*3
c*3
1
14
MICRO-LEVEL LABOR SUPPLY
Labor Supply in the Micro
An experiment: how do micro-level consumption/leisure choices
change as the real wage changes (assume t = 0 here for simplicity)
REAL WAGES: (W/P)1 < (W/P)2 < (W/P)3 < (W/P)4
leisure
c
slope = -(W/P)1
l*1
c*1
slope = -(W/P)2
l*2
c*2 slope = -(W/P)3
l*3 = l*4
c*3
slope = -(W/P)4
c*4
1
15
MICRO-LEVEL LABOR SUPPLY
Labor Supply in the Micro
An experiment: how do micro-level consumption/leisure choices
change as the real wage changes (assume t = 0 here for simplicity)
REAL WAGES: (W/P)1 < (W/P)2 < (W/P)3 < (W/P)4 < (W/P)5
leisure
c
slope = -(W/P)1
l*1
c*1
slope = -(W/P)2
l*2
c*2 slope = -(W/P)3
l*3 = l*4
c*3
slope = -(W/P)4
c*4
slope = -(W/P)5
c*5
l*5 1
16
MICRO-LEVEL LABOR SUPPLY
Labor Supply in the Micro
An experiment: how do micro-level consumption/leisure choices
change as the real wage changes (assume t = 0 here for simplicity)
REAL WAGES: (W/P)1 < (W/P)2 < (W/P)3 < (W/P)4 < (W/P)5
leisure
c
slope = -(W/P)1
l*1
c*1
slope = -(W/P)2
l*2
c*2 slope = -(W/P)3
l*3 = l*4
c*3
slope = -(W/P)4
c*4
slope = -(W/P)5
c*5
l*5
SUMMARY
1. For low levels of real wages, a rise in the real wage causes optimal leisure to decrease
2. For intermediate levels of real wages, a rise in the real wage causes optimal leisure to
remain unchanged
3. For high levels of real wages, a rise in the real wage causes optimal leisure to increase
1
17
MICRO-LEVEL LABOR SUPPLY
Labor Supply in the Micro
Using the relation n = 1 - l
labor
real
wage
n*1 n*2 n*3 = n*4
n*5
Backward-bending labor supply
curve at the micro level…
18
DECOMPOSING EFFECTS OF PRICE CHANGES
Micro Fundamentals
 Substitution effect
 General two-good case: if relative price of good 1 increases (i.e., P1/P2
increases), purchases of good 1 decrease
 Good 1 more expensive  buy less of it
 Application to consumption-leisure framework: if real wage W/P
increases (i.e., the relative price (opportunity cost) of leisure), choose
less leisure  choose to work more
 Income effect
 General two-good case: if total income increases (i.e., Y increases),
purchases of all goods increases
 Richer  buy more of everything
 Application to consumption-leisure framework: if real wage W/P
increases  total income increases (holding all else constant…) 
choose more leisure (leisure is a good)  choose to work less
Work in opposite
directions in C-L
framework
19
MICRO-LEVEL LABOR SUPPLY
Labor Supply in the Micro
Using the relation n = 1 - l
labor
real
wage
n*1 n*2 n*3 = n*4
n*5
Backward-bending labor supply
curve at the micro level…
Substitution effect
dominates the
income effect
Income effect
dominates the
substitution effect
Income effect and
substitution effect
roughly cancel
20
LABOR SUPPLY
Labor Supply in the Micro and the Macro
Using the relation n = 1 - l
labor
real
wage
n*1 n*2 n*3 = n*4
n*5
Backward-bending labor supply
curve at the micro level…
Substitution effect
dominates the
income effect
Income effect
dominates the
substitution effect
Income effect and
substitution effect
roughly cancel
labor
real
wage
…but not at the macro level
S
Individual-level labor supply function Aggregate-level labor supply function
Sum over all individuals
21
MACRO VS. MICRO LABOR QUANTITIES
Micro-Macro Connections

 Standard rep-agent framework offers an average theory of employment
 But not necessarily of unemployment
 Search and matching theory is a theory of unemployment (will come back to
this later…)
Aggregate Hours WorkedAverage hours
per worker
Number of
individuals working
=Aggregate Hours Worked
=
Average hours
per worker
Number of
individuals workingx
Micro studies measure
this
“Intensive margin” “Extensive margin”
Macro/representative-agent
framework typically focuses on
this
22
CONSUMPTION DEMAND
Consumption Demand in the Micro and the Macro
 Optimal choice of consumption was always rising as real wage was
rising
 Could have conducted the entire analysis assuming nominal W was
held fixed and nominal P was falling
 Which means real wage W/P is rising
 Result: Fall in P  rise in optimal c always
 Implies downward-sloping consumption demand function at the micro
level…
 …and at the aggregate level
 Consumption demand over two-thirds of aggregate demand in
developed countries
23
THE THREE MACRO (AGGREGATE) MARKETS
The Three Macro Markets
 Goods Markets
 Demand derived from “C-L framework”
 Labor Markets
 Supply derived from “C-L framework”
 Financial/Capital/Savings/Asset
Markets
c
P
labor
wage
capital
interest
rate
S
D
CONSUMPTION-SAVINGS
FRAMEWORK
(SNEAK PEEK)
CHAPTER 3 AND 4
25
THE MACROECONOMICS OF TIME
 Consumption-leisure model a static (i.e., one time period) model
 Dynamic frameworks the core of modern macroeconomic theory
 Explicit consideration of how economic
decisions/behaviors/outcomes unfold over multiple time periods
 Two-period framework (Chapters 3 and 4) the simplest possible
multi-period framework
 Will allow us to begin analyzing issues regarding interest rates and
inflation (phenomena that occur across time)
 Will allow us to think about credit restrictions and the “credit crunch”
 Infinite-period framework (Chapter 8)
 Allows a richer quantitative description of the macroeconomy
 Highlights the role of assets and the intersection between finance
and macroeconomics

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