Microeconomics II

class: center, middle, inverse, title-slide

.title[
# Microeconomics II
]
.subtitle[
## <div class="line-block">General Equilibirum and Economic Efficiency</div>
]
.author[
### Guillermo Woo-Mora
]
.date[
### <div class="line-block">Paris Sciences et Lettres<br />
Spring 2025</div>
]

---

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.center2[
# Introduction 
]

---
## Intro

Today we will review **conceptual tools** by which economists assess the desirability of market outcomes and the welfare and distributional eﬀects of government intervention

**Welfare economics**: provides the basis for judging the achievements of markets and policy makers in allocating resources (normative evaluation of markets and economic policy)

1) General Equilibrium (GE) Analysis `$\Rightarrow$` **Markets are interdependent**: Conditions in one can affect prices and outputs in others

2) Efficiency in Exchange `$\Rightarrow$` **First fundamental theorem in welfare econ**: The competitive equilibrium, maximizes social efficiency

3) (Normative statements of) Efficiency and Equity `$\Rightarrow$` **Second fundamental theorem in welfare econ**: under certain conditions, no conflict between efficiency and equity

4) Revise Efficiency in Production `$\Rightarrow$` **efficient use of inputs** in the
production process + GE to find the **prices that equate supply and demand in every market**

5) Revise Efficiency in Trade `$\Rightarrow$` account **comparative advantages** and potential gains of trade

6) Take stock

7) What are the problems with the points above

---
.center2[
# General Equilibrium Analysis 
]

---
## General Equilibrium Analysis

Before, we studied **partial equilibrium**: Determination of equilibrium prices and quantities in a market independent of effects from other markets.

**General equilibrium analysis**: 
--
 Simultaneous determination of the prices and quantities in all relevant markets, taking feedback effects into account.

In practice, a complete general equilibrium analysis, which evaluates the effects of a change in one market on all other markets, is not feasible. 
--
 Instead, we confine ourselves to two or three markets that are closely related
 
---
## Two Interdependent Markets

Suppose we have to markets: Movie tickets and DVD rentals. Substitutes: Watch movies at home or at theater.

At (partial) equilibrium:

.pull-left[
#### **Movie theaters**: `$P_M = 6$`
<img src="chapter16_files/figure-html/movies-01-1.png" width="150%" style="display: block; margin: auto;" />

]

.pull-right[
#### DVD Rentals: `$P_D = 3$`

<img src="chapter16_files/figure-html/dvd-01-1.png" width="150%" style="display: block; margin: auto;" />
]

---
## Two Interdependent Markets

Now suppose the government places a tax of $1 on each movie ticket purchased.

On partial equilibrium: supply curve for movies shifts upward by 1, from `$S_M$` to `$S^*_M$`

.pull-left[
#### **Movie theaters**: `$P_M = 6 \Rightarrow P'_M \approx 6.4$`
<img src="chapter16_files/figure-html/movies-02-1.png" width="150%" style="display: block; margin: auto;" />

]

.pull-right[
#### DVD Rentals: `$P_D = 3$`

<img src="chapter16_files/figure-html/dvd-02-1.png" width="150%" style="display: block; margin: auto;" />
]

Is that it?

---
## Two Interdependent Markets

Since the two markets are substitutes, the demand for DVDs will increase.

Higher movie price shifts the demand for DVDs from `$D_V$` to `$D'_V$`

.pull-left[
#### **Movie theaters**: `$P_M = 6 \Rightarrow P'_M \approx 6.4$`
<img src="chapter16_files/figure-html/movies-03-1.png" width="150%" style="display: block; margin: auto;" />

]

.pull-right[
#### DVD Rentals: `$P_D = 3 \Rightarrow P'_D \approx 3.4$`

<img src="chapter16_files/figure-html/dvd-03-1.png" width="150%" style="display: block; margin: auto;" />
]

Is that it?

---
## Two Interdependent Markets

Since the two markets are substitutes, the demand for movies will increase.

Higher DVD rental price shifts the demand for movies from `$D_M$` to `$D'_M$`

.pull-left[
#### **Movie theaters**: `$P'_M = \approx 6.4 \Rightarrow P''_M = 7$`
<img src="chapter16_files/figure-html/movies-04-1.png" width="150%" style="display: block; margin: auto;" />

]

.pull-right[
#### DVD Rentals: `$P_D = 3 \Rightarrow P'_D \approx 3.4$`

<img src="chapter16_files/figure-html/dvd-04-1.png" width="150%" style="display: block; margin: auto;" />
]

---
## Reaching General Equilibrium

**General equilibrium requires simultaneous analysis of both markets**, Since changes in one market feed back into the other, affecting final prices and quantities.

.pull-left[
#### **Movie theaters**: `$\Rightarrow \{P^*, Q^*\}$` such that `$S^*_M = D^*_M$`
<img src="chapter16_files/figure-html/movies-05-1.png" width="150%" style="display: block; margin: auto;" />

]

.pull-right[
#### DVD Rentals: `$\Rightarrow \{P^*, Q^*\}$` such that `$S^*_D = D^*_D$`

<img src="chapter16_files/figure-html/dvd-05-1.png" width="150%" style="display: block; margin: auto;" />
]

- Partial equilibrium underestimates impacts, but GE analysis shows a larger increase due to intermarket feedback.

---
## Economic Efficiency

Competitive markets are economically efficient: they maximize aggregate consumer and producer surplus (Chapter 9).

---
## Economic Efficiency

How does economic efficiency apply when considering the interconnected nature of markets across different systems—whether open or closed, free or regulated, or market-based or planned?

---
.center2[
# Efficiency in Exchange 
]

---
## Efficiency in Exchange

Consider an **exchange economy**: Market in which two or more consumers (countries) trade two goods among themselves.

The two goods are initially allocated so that both consumers can make themselves better off by trading with each other
--
: the initial allocation of goods is economically inefficient.

**Pareto efficient allocation**: Allocation of goods in which no one can be made better off unless someone else is made worse off.

- Notice this is different than 'economic efficiency' as we previously studied
 
 - With Pareto efficiency, we know that there is no way to improve the well-being of both individuals (if we improve one, it will be at the expense of the other), but we cannot be assured that this arrangement will maximize the joint welfare of both individuals.

---
## The Advantages of Trade

Voluntary trade between two people or two countries is mutually beneficial.

Example: two-person exchange, assuming that exchange itself is costless. 
--
Suppose James and Karen have 10 units of food and 6 units of clothing between them.

| Individual | Initial Allocation |
|------------|--------------------|
| James      | 7F, 1C             |
| Karen      | 3F, 5C             |

To decide whether a trade would be advantageous, **we need to know their preferences for food and clothing**.

.pull-left[
Karen has a lot of clothing and little food:

Suppose she's willing to give up 3 units of clothing for 1 unit of food.

**Karen's MRS of food for clothing is 3**
]

.pull-right[
James has a loot of food and little clothing:

He will give up only 1/2 a unit of clothing to get 1 unit of food.

**James’s MRS of food for clothing is 1/2**
]

Trade is beneficial because James values clothing more, while Karen values food more.

---
## The Advantages of Trade

Voluntary trade between two people or two countries is mutually beneficial.

Suppose Karen offers James 1 unit of clothing for 1 unit of food, and James agrees.

| Individual | Initial Allocation | Trade       |
|------------|--------------------|-------------|
| James      | 7F, 1C             | −1F, +1C     |
| Karen      | 3F, 5C             | +1F, −1C     |

---
## The Advantages of Trade

Voluntary trade between two people or two countries is mutually beneficial.

Suppose Karen offers James 1 unit of clothing for 1 unit of food, and James agrees.

| Individual | Initial Allocation | Trade       | Final Allocation |
|------------|--------------------|-------------|------------------|
| James      | 7F, 1C             | −1F, +1C     | 6F, 2C           |
| Karen      | 3F, 5C             | +1F, −1C     | 4F, 4C           |

Both benefit from trade: James gains more clothing, and Karen gains more food, aligning with their preferences.

When consumers have different MRS, trade improves efficiency; equal MRS indicate an efficient allocation.

---
## The Edgeworth Box Diagram

**Edgeworth box Diagram**: showing all possible allocations of either two goods between two people or of two inputs between two production processes.

Horizontal axis: number of units of food. Vertical axis: the units of clothing.

---
## The Edgeworth Box Diagram

**Edgeworth box Diagram**: showing all possible allocations of either two goods between two people or of two inputs between two production processes.

Length of the box 10 units of food and 6 of clothing, total quantities available.

---
## The Edgeworth Box Diagram

James’s holdings are read from the origin at `$O_{James}$`.

---
## The Edgeworth Box Diagram

Karens’s holdings are read in the reverse direction from the origin at `$O_{Karen}$`.

---
## The Edgeworth Box Diagram

Initial allocation

---
## The Edgeworth Box Diagram

Initial food allocation

---
## The Edgeworth Box Diagram

Initial clothing allocation

---
## The Edgeworth Box Diagram

After trade

---
## The Edgeworth Box Diagram

Food allocation after trade

---
## The Edgeworth Box Diagram

Clothing allocation after trade

---
## The Edgeworth Box Diagram

---
## Efficient Allocations

A trade from *A* to *B* thus made both Karen and James better off.
--
 But is *B* an efficient allocation? The answer depends on both MRS.

---
## Efficient Allocations

At point *A*, James's indifference curve is `$U_K^A$`.

---
## Efficient Allocations

At point *A*, Karen's indifference curve is `$U_J^A$`. Note: Karen’s indifference curves are rotated 180°, placing her origin at the top right of the box.

---
## Efficient Allocations

The shaded area shows all allocations that make both James and Karen better off than at A—i.e., all mutually beneficial trades.

---
## Efficient Allocations

Any trade moving outside the shaded area from A would harm at least one consumer and should be avoided.

---
## Efficient Allocations

What happens with trade? Point *B*.

---
## Efficient Allocations

What happens with trade? At point *B*, James's indifference curve is `$U_J^B$`.

---
## Efficient Allocations

What happens with trade? At point *B*, Karen's indifference curve is `$U_K^B$`.

---
## Efficient Allocations

Moving from *A* to *B* is mutually beneficial, but it is not efficient because the indifference curves intersect.

---
## Efficient Allocations

Starting at *B*, James is willing to trade food for clothing to improve or maintain his utility, and many such trades are possible.

---
## Efficient Allocations

Starting at *B*, Karen is willing to trade clothing for food, with many options that would make her better off.

---
## Efficient Allocations

**Even if a trade from an inefficient allocation makes both people better off, the new allocation is not necessarily efficient.**

---
## Efficient Allocations

Suppose that from B the additional trade is made, up to point *C*, where James giving uo another unit of food to get 1/2 clothing.

---
## Efficient Allocations

At point *C*, the indifference curves are tangent `$\Rightarrow$` **Pareto efficient outcome**: one person cannot be made better off without making the other person worse off.

---
## The Contract Curve

**Contract curve**: Curve showing all efficient allocations of goods between two consumers, or of two inputs between two production functions.

---
## The Contract Curve

.pull-left[

- Pareto efficiency means no one can be made better off without making someone else worse off.

- a modest goal: we should make all mutually beneficial exchanges, but it does not say which exchanges are best.
	
  -	multiple outcomes can be efficient, but we can’t say which is better without knowing preferences (nor initial endowments).

- Efficiency doesn’t imply fairness or optimality, just that no mutual gains remain.
	
- Efficiency can still improve if harmful changes are paired with compensating ones.

]

.pull-right[
<img src="imgs/f16.6.png" width="100%" style="display: block; margin: auto;" />

The contract curve shows all efficient allocations where no further mutually beneficial trade is possible.

]

---
## Consumer Equilibrium in a Competitive Market

In a two-person exchange, the outcome can depend on the bargaining power of the two parties.

In competitive markets, numerous actual or potential buyers and sellers exist, and each accepts the market price as given, deciding only the quantity to buy or sell.

We can illustrate how competitive markets lead to efficient exchange using the Edgeworth box by assuming many individuals like James and Karen. This lets us treat each as a price taker, even in a two-person diagram.

---
## Consumer Equilibrium in a Competitive Market

---
## Consumer Equilibrium in a Competitive Market

Opportunities for trade when we start at the allocation given by point *A*.

---
## Consumer Equilibrium in a Competitive Market

Suppose they want to achieve allocation *C* under trade, and increase their satisfaction by moving to higher indifference curves.

---
## Consumer Equilibrium in a Competitive Market

We need (relative) prices so that the quantity of food demanded by
each Karen is equal to the quantity of food that each James wishes to sell.

---
## Consumer Equilibrium in a Competitive Market

Note: The actual prices do not matter; what matters is the price of food relative to the price of clothing (in this example, `$-0.75$`, different than the example in the book).

---
## Consumer Equilibrium in a Competitive Market

**An equilibrium is a set of prices at which the quantity demanded equals the quantity supplied in every market.** This is also a **competitive equilibrium** because all are price takers.

---
## Consumer Equilibrium in a Competitive Market

Not all prices are consistent with equilibrium.

---
## Consumer Equilibrium in a Competitive Market

The flatter price line implies a low relative price of food, causing excess demand for food and excess supply of clothing. This puts upward pressure on the price of food.

---
## Consumer Equilibrium in a Competitive Market

The steeper price line implies a high relative price of food, leading to excess supply of food and excess demand for clothing. This pushes the price of food downward.

---
## The Economic Efficiency of Competitive Markets

We can now understand one of the fundamental results of microeconomic analysis.

*Invisible Hand* or **first theorem of welfare economics**: **An allocation in a competitive equilibrium is Pareto efficient**
 
---
## The Economic Efficiency of Competitive Markets

*Invisible Hand* or **first theorem of welfare economics**: **An allocation in a competitive equilibrium is Pareto efficient**

Note: *theoretical result* 
--
, holds in an exchange framework and in a general equilibrium setting in which all markets are perfectly competitive.

---
## The Economic Efficiency of Competitive Markets

*Invisible Hand* or **first theorem of welfare economics**: **An allocation in a competitive equilibrium is Pareto efficient**

.pull-left[
> If everyone trades in the competitive marketplace, all mutually beneficial trades will be completed and the resulting equilibrium allocation of resources will be Pareto efficient.

1. Because the indifference curves are tangent, all marginal rates of substitution between consumers are equal.

2. Because each indifference curve is tangent to the price line, each person’s MRS of clothing for food is equal to the ratio of the prices of the two goods

]

.pull-right[
<img src="chapter16_files/figure-html/eq-eff03-1.png" width="120%" style="display: block; margin: auto;" />

`$$MRS^J_{FC} = P_F / P_C = MRS^K_{FC}$$` 
]

---
.center2[
# Equity and Efficiency
]

---
## Equity and Efficiency

- Different efficient allocations of goods are possible

- Perfectly competitive economy generates a Pareto efficient allocations

- A Pareto efficient allocation means no one can be made better off without making someone else worse off

- There are many Pareto efficient allocations

**How do we decide what is the most equitable allocation?**

---
## The Utility Possibilities Frontier

Recall the contract curve:

---
## The Utility Possibilities Frontier

Curve showing all efficient allocations of resources measured in terms of the utility levels of two individuals.

Edgeworth box in a different form: James’s utility is measured on the horizontal axis and Karen’s on the vertical axis.

---
## The Utility Possibilities Frontier

Curve showing all efficient allocations of resources measured in terms of the utility levels of two individuals.

Point `$O_J$` is one extreme at which James has no goods and therefore zero utility.

---
## The Utility Possibilities Frontier

Curve showing all efficient allocations of resources measured in terms of the utility levels of two individuals.

Point `$O_K$` is the opposite extreme at which Karen has no goods.

---
## The Utility Possibilities Frontier

Curve showing all efficient allocations of resources measured in terms of the utility levels of two individuals.

Because all other points on the frontier (*E*, *F*, and *G*) correspond to points on the contract curve, one person cannot be made better off without making the other worse off.

---
## The Utility Possibilities Frontier

Curve showing all efficient allocations of resources measured in terms of the utility levels of two individuals.

Point *H* is inefficient because any trade within the shaded area would improve the well-being of one or both individuals.

---
## The Utility Possibilities Frontier

Curve showing all efficient allocations of resources measured in terms of the utility levels of two individuals.

Point *L* would make both individuals better off, but it is unattainable because the available resources are insufficient to reach the utility levels it represents.

---
## The Utility Possibilities Frontier

Compare point *H* with *F* and *E*.

Both *F* and *E* are efficient. Moving from *H* to each makes one person better off without making the other worse off.

Thus, it might be inequitable for James, Karen, or both to get *H* instead of *F* or *E*.

---
## The Utility Possibilities Frontier

Now suppose *H* and *G* are the only possible allocations. Is *G* more equitable than *H*?

Depends on personal tastes.

Note: **one Pareto inefficient allocation of resources may be more equitable than another Pareto efficient allocation.**

---
## Social Welfare Functions

In economics, we often use a **social welfare function** to describe the well-being of society as a whole in terms of utilities of individual members.

> Measure describing the well-being of society as a whole in
terms of the utilities of individual members.

1. Egalitarian - all members of society receive equal amounts of goods

2. Rawlsian - maximize the utility of the least-well-off person: `$SWF = min(U_1, U_2, \cdots, U_N)$`

3. Utilitarian - maximize the total utility of all members of society: `$SWF = U_1 + U_2 + \cdots + U_N$`

4. Market - oriented—the market outcome is the most equitable

---
## Equity and Perfect Competition

A competitive equilibrium leads to a Pareto efficient outcome that may or may not be equitable.

Efficient allocations aren’t always equitable, so governments often intervene to promote equity through income redistribution, taxes, or public services: 1) progressive income or wealth tax, 2) redistribution programs, or 3) provide public services

---
## Equity and Perfect Competition

.pull-left[
**second theorem of welfare economics**:

> If individual preferences are convex, then every Pareto efficient allocation (every point on the contract curve) is a competitive equilibrium for some initial allocation of goods.

Any equilibrium deemed to be equitable can be achieved by a suitable distribution of resources among individuals and that such a distribution need not in itself generate inefficiencies.

]

.pull-right[
<img src="chapter16_files/figure-html/unnamed-chunk-14-1.png" width="120%" style="display: block; margin: auto;" />

Reallocate initial endowments
]

Unfortunately, there are behavioral responses to governmental intervention. Then, one must choose between equity and efficiency.

Economics try to provide causal estimates of the actual cost of these trade-offs to inform policy. [See lessons on unconditional cash transfers](https://voxdev.org/topic/social-protection/what-broad-lessons-have-we-learned-115-studies-unconditional-cash-transfers).

---
## Illustration of 2nd Welfare Theorem Fallacy

Suppose the following economy: 50% disabled (unable to work, earn 0), 50% able (can work and earn 100)

**Free Market Outcome:** Disabled: 0, Able: 100

#### 2nd Welfare Theorem Assumption:

Government can **distinguish disabled from able** (even if able do not work)

- Tax able by $50 (regardless of work status)  
- Transfer $50 to each disabled person  
- Able people continue working (if not, they still owe 50 with 0 income)

Real World Limitation: Government **cannot easily distinguish** disabled from non-working able

- 50 tax on workers + 50 transfer to non-workers affects work incentives  
- Government **cannot fully redistribute**  
- **Trade-off** between equity and size of the pie

---
.center2[
# Efficiency in Production
]

---
## Efficiency in Production

We have described the conditions required to achieve an efficient allocation in the exchange of two goods.

We now study the efficient use of inputs in the production process.

We assume that:

- there are fixed total supplies of two inputs, **labor** and **capital**, which are needed to produce the same two products, food and clothing

- many consumers own the inputs to production (including labor) and earn income by selling them

- the income, in turn, is allocated between the two goods

Not a new concept; we studied that a production function represents the maximum output that can be achieved with a given set of inputs. 
--
 Here we extend the concept to the production of two goods rather than one.

---
## Input Efficiency

Various combinations of inputs that can be used to produce each of the two outputs.

A particular allocation of inputs into the production process is **technically efficient** if the output of one good cannot be increased without decreasing the output of another good.

.pull-left[
#### Labor markets

If competitive `$\Rightarrow$` wage rate `$w$` will be the same in all industries

]

.pull-right[
#### Capital markets

If competitive `$\Rightarrow$` rental rate of capital `$r$` will be the same whether capital is used in the food or clothing industry

]

If producers of food and clothing minimize production costs, will use combinations of labor and capital such that:

`$$\frac{MP_L}{MP_K} = w/r = MRTS_{LK}$$`

where  MRTS stands for Marginal Rate of Technical Substitution of labor for capital.

Remember this is the slope of a firm's isoquant.