Transcript Lecture02a

Lecture # 02-a
Introduction (cont.)
Lecturer: Martin Paredes
1. Microeconomic Modeling
• Elements of models
• Solving the models
2. The Limits of Microeconomic Analysis
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All microeconomic models rely on three
analytical tools:
 Constrained optimisation
 Equilibrium analysis
 Comparative statics
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Constrained optimisation problems
usually have two parts:
Objective function
A set of constrains
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Definition: The Objective Function specifies what the
agent cares about and wants to optimize
Examples:
• A consumer cares about maximizing his satisfaction
• The manager cares about:
• Raising profits
• Reducing costs
• Increasing “power”
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Definition: Limits placed on the resources available to the
agent
Examples:
• The manager’s budget is €1M
• The consumer’s income is €3000
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The behavior of an agent can be modeled as
optimizing the objective function, subject to his
various constraints.
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Example: Consumer purchases
• The consumer
• Chooses Food (F) and Clothing (C)
• Take as given his Income (I), the Price of food (PF)
and the Price of clothing (PC)
• Satisfaction from purchases: S = (FC)1/2
• Objective function:
Max S = (FC)1/2 subject to: PFF + PCC < I
(F,C)
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F
Example: Consumer Purchases
PFF + PCC = I
0
C
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F
Example: Consumer Purchases
PFF + PCC = I
(FC)1/2 = S1
0
C
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F
Example: Consumer Purchases
PFF + PCC = I
(FC)1/2 = S1
(FC)1/2 = S0
0
C
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F
Example: Consumer Purchases
PFF + PCC = I
S2 > S1 > S0
(FC)1/2 = S2
(FC)1/2 = S1
(FC)1/2 = S0
0
C
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Another Example: Advertising Spots
Suppose the manager of a beer company wants to decide the
firm’s advertising spots.
Budget = €1m to allocate between TV ( T ) and radio ( R )
Problem: Max B(T,R)
(T,R)
subject to: pTT + pRR < €1m
where: B is "barrels“ and pT, pR are the prices of TV and radio
advertising, respectively.
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Total Spent
New Beer Sales Generated
TV
Radio
$ 0
0
0
$100,000
4,750
950
$200,000
9,000
1,800
$300,000
12,750
2,550
$400,000
16,000
3,200
$500,000
18,750
3,750
$600,000
21,000
4,200
$700,000
22,750
4,550
$800,000
24,000
4,800
$900,000
24,750
4,950
$1,000,000
25,000
5,000
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Definition:
Equilibrium is a state that will
continue indefinitely as long as the
exogenous factors remain unchanged.
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Price per pound
Example: The Market for Coffee Beans
Supply (P,W)
Q*
Quantity, pounds
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Price per pound
Example: The Market for Coffee Beans
Supply (P,W)
•
Demand (P,I)
Q*
Quantity, pounds
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Price per pound
Example: The Market for Coffee Beans
Supply (P,W)
P*
•
Demand (P,I)
Q*
Quantity, pounds
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Definition:
In this example, Equilibrium is defined as the
point where demand equals supply in this
market
(i.e., the point where the demand and supply
curves cross)
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Definition:
A comparative statics analysis compares
the equilibrium state of a system
before a change in the exogenous variables
to the equilibrium state after the change.
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Price per pound
Example: Coffee Beans, revisited
Supply (P,W)
•
Demand (P,I)
Quantity, pounds
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Price per pound
Example: Coffee Beans, revisited
Supply (P,W)
New Supply (P,W)
•
•
Demand (P,I)
Quantity, pounds
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Price per pound
Example: Coffee Beans, revisited
Supply (P,W)
New Supply (P,W)
P*
P**
•
•
Demand (P,I)
Q* Q**
Quantity, pounds
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F
Example: Consumer choice, revisited
PFF + PCC = I0
0
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C
F
Example: Consumer choice, revisited
PFF + PCC = I0
(FC)1/2 = S0
•
0
C** C*
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C
Example: Consumer choice, revisited
F
PFF + PCC = I0
(FC)1/2 = S0
•
•
PFF + PCC = I1
0
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C
Example: Consumer choice, revisited
F
PFF + PCC = I0
(FC)1/2 = S0
•
0
•
(FC)1/2 = S1
PFF + PCC = I1
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C
Example: Consumer choice, revisited
F
PFF + PCC = I0
(FC)1/2 = S0
F*
F**
0
•
S0 > S1
I0 > I1
•
C** C*
(FC)1/2 = S1
PFF + PCC = I1
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C
Definition: Positive Analysis
• Can explain what has happened due to an
economic policy, or
• Can predict what might happen due to an
economic policy.
Definition:
Normative analysis is an analysis of
what should be done
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Examples:
• “Should we increase income equality rather than focus
on economic efficiency?”
• “Should we impose a progressive income tax or a sales
tax to increase income equality?”
• “Will a progressive income tax reduce aggregate hours
worked?”
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