1. The Market Economy

 
 

1. The Market Economy 

Fall 2008

 
 

Outline 

• A.  Introduction: What is Efficiency?
• B.  Supply and Demand (1 Market)
• C.  Efficiency of Consumption (Many Markets)
• D.  Production Efficiency (Many Markets)

 

 
 

A. Introduction 

Economics is based on assumptions of maximization and equilibrium:

• Individuals taking decisions to maximize profit or utility. (individualistic)
• These decisions interact in markets and we use the notion of equilibrium to predict what is the outcome.

 

We build  models who gets what and why they get it. (How resources are allocated.)

These have testable implications.

 
 

Key themes 

Incentives:  Why do optimizers do what they do?

Information:  What do individuals know and is this useful? 

Surprising idea: Individual optimization can promote the common good. (In certain cases.) 

Markets and other domains where individuals interact aggregate individual’s decisions and information. 

 

 
 

Pareto Efficiency 

Definition: An allocation of resources is Pareto Efficient if it is not possible to reallocate resources to make everyone better off. 

How do we measure better off?

    We use Utility to measure welfare/happiness.

 

 
 

Utility Possibilities: What is Feasible 

  

1’s Utility 

2’s Utility

 
 

Utility Possibilities: What is Feasible 

  

1’s Utility 

2’s Utility 

Allocations

 
 

Pareto efficiency: There is no waste 

  

1’s Utility 

2’s Utility 

Pareto efficient Allocation

 
 

Equity: equal shares 

  

1’s Utility 

2’s Utility 

U₁ = U₂

 
 

Utilitarianism: Maximize U(1)+U(2) 

  

1’s Utility 

2’s Utility

 
 

Rawls: Maximize min{U(1),U(2)} 

  

1’s Utility 

2’s Utility

 
 

Example: Efficiency in Exchange 

A buyer values the good at 4 (and gets 0 otherwise).

A seller who values the good at 2 (and gets 0 otherwise).

They can trade at the price p. 

                                  Buyer   Seller

Seller keeps the good no trade 0  2

Buyer pays seller p and  4-p  p

buyer gets the good 
 

Q: What values of p is trade better than no trade?

 
 

B. The Supply and Demand Fable 

Suppose you have:

• 100 people each wanting a cup of coffee, but valuing the coffee different amounts.
• 80 people willing to make a cup, but with different costs.

 

Your job is to decide who should get a cup and who should make it. 

What do you want to avoid:

    (1)  A $5 buyer not getting a coffee but a $1 buyer getting one.

          (allocative inefficiency)

    (2) A $1 seller not making a coffee but a $5 seller getting one.

          (production inefficiency)

    (3) A $3 seller providing coffee to a $2 buyer. (over provision)

    (4) A $4 buyer not getting a coffee although there are sellers with $2 costs  not making coffees. (under provision)

    (5) Some coffee not being consumed by anyone.  

 

 
 

Possible mechanisms 

(1) Central Planning/Fiat:    (Centralized)

    Tell people what to do.  (After first having tried to find out what people want.) Likely to fail all the above tests. 

(2) Organize an Auction     (Centralized)

    Tell buyers and sellers to submit bids – likely to fail all tests. 

(3) Organize a Market   (Centralized & Decentralized)

    Call out a price for coffee.  

(4) Put them all in a room and let them get on with it!

                                              (Decentralized)

 
 

  

P 

Q of Coffee 

Demand (100)

 
 

  

P 

Q of Coffee 

Supply (80)

 
 

  

P 

Q of Coffee 

Demand 

Supply

 
 

  

P 

Q of Coffee 

Demand 

Supply

 
 

  

P 

Q of Coffee 

Demand 

Supply

 
 

  

P 

Q of Coffee 

Demand 

Supply

 
 

  

P 

Q of Coffee 

Demand 

Supply

 
 

Conclusions 

If

1. a market is organized,
2. the market is perfectly competitive,
3. price is at the equilibrium,

 

then 

full efficiency is achieved.

 
 

C. Efficiency of Economies with Many Goods (No Production) 

Consumer Behaviour with Many Goods 

Quantity of A 

Quantity of B

 
 

C. Efficiency with Many Goods 

Indifference Curves 

Quantity of A 

Quantity of B 

utility =2

 
 

C. Efficiency with Many Goods 

Indifference Curves 

Quantity of A 

Quantity of B 

utility =3

 
 

C. Efficiency with Many Goods 

indifference curves 

Quantity of A 

Quantity of B 

utility =4

 
 

C. Efficiency with Many Goods 

Indifference Curves 

Quantity of A 

Quantity of B 

Higher Utility

 
 

Budget Constraints 

  

Quantity of A 

Quantity of B 

With $10 can afford 10 = p_AX(Units of A) + p_BX(Units of B) 

  

10 = p_AQ_A + p_B Q_B

 

 
 

Budget Constraints 

  

Quantity of A 

Quantity of B 

With $10 can afford 10 = p_AX(Units of A) + p_BX(Units of B)

 
 

Budget Constraints 

  

Quantity of A 

Quantity of B 

With $10 can afford 10 = p_AX(Units of A) + p_BX(Units of B)

 
 

Consumer Optimum 

  

Quantity of A 

Quantity of B

 
 

Consumer Optimum 

  

Quantity of A 

Quantity of B 

Here Slopes are equal

 
 

Equal Slopes 

Slope of Budget Line:

                                  = - p_A /p_B 

Slope of Indifference Curve

                                  = - MU_A / MU_B

 
 

Equal Slopes 

Slope of Budget Line:

                                  = - p_A /p_B 

Slope of Indifference Curve

                                  = - MU_A / MU_B

  

This is called:

    “The Marginal Rate of Substitution”

 
 

Equal Slopes 

Slope of Budget Line:

                                  = - p_A /p_B 

Slope of Indifference Curve

                                  = - MU_A / MU_B

Equality Implies

             MU_A / MU_B  =  p_A /p_B

Or

             MU_B/ p_B  =  MU_B /p_B

Interpretation:

                Extra utility from $1 = Extra utility from $1

                       spent on A    spent on B

 
 

At Last: Efficiency with Many Goods 

Imagine 2 people: person I (she) and person II (he).

They begin life with:

                      Good A Good B

Person I  5 units  1 unit

Person II  1 unit  5 units 

These are called endowments.

They want to trade to achieve better bundles.

 
 

Their Resources 

  

I’s Quantity of A 

I’s Quantity of B 

II’s Quantity of B 

II’s Quantity of A

 
 

Their Endowment 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

I’s Preferences 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

II’s Preferences 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Putting Preferences together 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Pareto efficiency: Is where cannot make I better off with out making II worse off. 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Pareto efficiency: Is where cannot make I better off with out making II worse off. 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Pareto efficiency: Is where cannot make I better off with out making II worse off. 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Pareto efficiency: Is where cannot make I better off with out making II worse off. 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Pareto efficiency: Is where cannot make I better off with out making II worse off. 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Allocation of Resources is efficient if 

    Slope of I’s Indifference     =  Slope of II’s Indifference  Curve      Curve 

                I’s MRS     =  II’s MRS 

          MU(I)_A / MU(I)_B  =  MU(II)_A / MU(II)_B

Or

          MU(I)_A / MU(II)_A  =  MU(I)_B / MU(II)_B 

Extra utility I gets from    Extra utility I gets from

small increase in A at the =  small increase in B at the

expense of II’s small decrease   expense of II’s small decrease

in A.     in B.

 
 

All the Pareto efficient places  

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

These join to give the Contract Curve  

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Pareto efficiency: Utility Possibilities 

  

I’s Utility 

II’s Utility 

Pareto efficient Allocation

 
 

D. Production Efficiency 

One firm uses inputs:

          Land and Labour to produce good A 

Another firm:

          uses Land and Labour to produce good B. 

 

 
 

Production Functions & Isoquants 

  

Quantity of Labour 

Quantity of land 

Output = 1 Unit of A

 
 

Production Functions & Isoquants 

  

Quantity of Labour 

Quantity of land 

Output = 1 Unit of A 

Output = 2 Unit of A

 
 

Production Functions & Isoquants 

  

Quantity of Labour 

Quantity of land 

Output = 1 Unit of A 

Output = 3 Unit of A 

Output = 2 Unit of A

 
 

Production Functions & Isoquants 

  

Quantity of Labour 

Quantity of land 

Output = 1 Unit of A 

Output = 3 Unit of A 

Output = 2 Unit of A 

Output = 5 Unit of A 

Output = 4 Unit of A

 
 

Most Efficient way of producing Output =3 

  

Quantity of Labour 

Quantity of land 

$8 = P_L Q_L+ P_N P_N

 
 

Most Efficient way of producing Output =3 

  

Quantity of Labour 

Quantity of land 

$9 = P_L Q_L+ P_N P_N 

$8 = P_L Q_L+ P_N P_N

 
 

Most Efficient way of producing Output =3 

  

Quantity of Labour 

Quantity of land 

$10 = P_L Q_L+ P_N P_N 

$9 = P_L Q_L+ P_N P_N 

$8 = P_L Q_L+ P_N P_N

 
 

Most Efficient way of producing Output =3 

  

Quantity of Labour 

Quantity of land 

Output = 3 Unit of A

 
 

Most Efficient way of producing Output =3 

  

Quantity of Labour 

Quantity of land 

Output = 3 Unit of A

 
 

Most Efficient way of producing Output =3 

  

Quantity of Labour 

Quantity of land 

Here Slopes are equal 

Output = 3 Unit of A

 
 

SLOPES ARE EQUAL SO: 

Slope of Isoquant

                      = - MP_N /MP_L  

                      = “Marginal rate of technical substitution”

Slope of Cost Line

                      =  - P_N /P_L 

Equal Slopes    MP_N /MP_L   =  P_N /P_L

or

                      MP_N /P_N   =  MP_L /P_L

 
 

Production Functions & Isoquants 

  

Quantity of Labour 

Quantity of land 

Here Slopes are equal 

Output = 1 Unit of A 

Output = 3 Unit of A 

Output = 2 Unit of A 

Output = 5 Unit of A 

Output = 4 Unit of A

 
 

Many Firms Producing  

  

Firm 1’s Labour 

Firm 1’s Land 

Firm II’s Land 

Firm II’s Labour

 
 

Many Firms Producing  

  

Firm 1’s Labour 

Firm 1’s Land 

Firm II’s Land 

Firm II’s Labour

 
 

Many Firms Producing: Efficient Production 

  

Firm 1’s Labour 

Firm 1’s Land 

Firm II’s Land 

Firm II’s Labour

 
 

SLOPES ARE EQUAL SO: 

Slope of Isoquant Firm I

                      = - MP(I)_N /MP(I)_L  

                      = “Marginal rate tech substitution (I)” 

Slope of Isoquant Firm II

                      = - MP(II)_N /MP(II)_L  

                      = “Marginal rate tech substitution (I)” 

Equal Slopes    MP(I)_N /MP(I)_L  = MP(II)_N /MP(II)_L  

or

                       MP(I)_N /MP(II)_N  = MP(I)_L /MP(II)_L

 
 

Many Firms Producing: Efficient Production 

  

Firm 1’s Labour 

Firm 1’s Land 

Firm II’s Land 

Firm II’s Labour

 
 

Production Possibility Frontier 

  

Firm 1’s Labour 

Firm 1’s Land 

Firm II’s Land 

Firm II’s Labour

 
 

Production Possibilities: What is Feasible 

  

Firm 1’s Output 

Firm 2’s Output

 
 

Production Possibilities: What is Feasible 

  

Firm 1’s Output 

Firm 2’s Output 

Slope of this line represents how economy is able to move from production of 2 into 1 =

Marginal Rate of Transformation

 
 

At Last: Production Efficiency with Many Goods and One Consumer 

  

Quantity of A 

Quantity of B 

Higher Utility 

How the consumer values goods

 
 

What can be produced 

  

Firm 1’s Output 

Firm 2’s Output

 
 

Maximizing Utility given Production 

  

Quantity of A 

Quantity of B 

Higher Utility 

How the consumer values goods

 
 

Slope of Indifference = Slope of Production Possibilities = Ratio of Prices 

  

Quantity of A 

Quantity of B 

Higher Utility 

How the consumer values goods

 
 

Efficiency with Many Goods and Production 

Slope of Indifference = Marginal Rate of Substitution 

Equals 

Slope of Production Possibilities = Marginal Rate of Transformation

Equals 

Ratio of Prices

 

 
 

Efficiency with Many Goods and Production 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5

 
 

Many Firms Producing: What is produced is determined by input prices 

  

Firm 1’s Labour 

Firm 1’s Land 

1 

5 

Firm II’s Land 

Firm II’s Labour 

1 

5

 
 

Their Preferences 

  

Quantity of A 

Quantity of B 

1 

5 

II’s Quantity of B 

II’s Quantity of A 

1 

5