Lecture # 02-aLecture # 02-a

Introduction (cont.)Introduction (cont.)

Lecturer: Martin ParedesLecturer: Martin Paredes

2

1. Microeconomic Modeling

• Elements of models

• Solving the models

2. The Limits of Microeconomic Analysis

3

All microeconomic models rely on three analytical tools: Constrained optimisation Equilibrium analysis Comparative statics

4

Constrained optimisation problems usually have two parts: Objective function A set of constrains

5

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”

6

Definition: Limits placed on the resources available to the agent

Examples:• The manager’s budget is €1M• The consumer’s income is €3000

7

The behavior of an agent can be modeled asoptimizing the objective function, subject to hisvarious constraints.

8

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)

9

Example: Consumer Purchases

PFF + PCC = I

F

C0

10

Example: Consumer Purchases

(FC)1/2 = S1

PFF + PCC = I

F

C0

11

Example: Consumer Purchases

(FC)1/2 = S1

(FC)1/2 = S0

PFF + PCC = I

F

C0

12

Example: Consumer Purchases

(FC)1/2 = S1

(FC)1/2 = S2

PFF + PCC = I

F

C0

S2 > S1 > S0

(FC)1/2 = S0

13

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.

14

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

15

Definition: Equilibrium is a state that will continue indefinitely as long

as the exogenous factors remain unchanged.

16

Example: The Market for Coffee BeansPrice per pound

Quantity, pounds

Supply (P,W)

Q*

17

Example: The Market for Coffee BeansPrice per pound

Quantity, pounds

Supply (P,W)

Demand (P,I)

•

Q*

18

Example: The Market for Coffee BeansPrice per pound

Quantity, pounds

Supply (P,W)

Demand (P,I)

•

Q*

P*

19

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)

20

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.

21

Price per pound

Quantity, pounds

Supply (P,W)

Demand (P,I)

•

Example: Coffee Beans, revisited

22

Example: Coffee Beans, revisited

Price per pound

Quantity, pounds

Supply (P,W)

Demand (P,I)

•

New Supply (P,W)

•

23

Price per pound

Quantity, pounds

Supply (P,W)

Demand (P,I)

•

Q*

P*

New Supply (P,W)

•

Q**

P**

Example: Coffee Beans, revisited

24

Example: Consumer choice, revisited

PFF + PCC = I0

F

C0

25

(FC)1/2 = S0

PFF + PCC = I0

F

C0

•

C** C*

Example: Consumer choice, revisited

26

(FC)1/2 = S0

PFF + PCC = I0

F

C0

••

PFF + PCC = I1

Example: Consumer choice, revisited

27

(FC)1/2 = S0

(FC)1/2 = S1

PFF + PCC = I0

F

C0

••

PFF + PCC = I1

Example: Consumer choice, revisited

28

(FC)1/2 = S0

(FC)1/2 = S1

PFF + PCC = I0

F

C0

S0 > S1

••

C** C*

F*

F**

PFF + PCC = I1

I0 > I1

Example: Consumer choice, revisited

29

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

30

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?”