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Walras' Law (Market Value)

Calculates the value of excess demand for a single market, a component of Walras' Law.

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V_{i} = p_{i} E_{i}

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Core idea

Overview

Walras' Law states that in a general equilibrium model, the sum of the values of excess demands across all markets must be zero. This calculator focuses on computing the value of excess demand ($p_i E_i$) for a specific market $i$, which is a fundamental building block for understanding the overall market equilibrium condition. It helps in analyzing individual market contributions to the aggregate excess demand.

When to use: Use this to calculate the monetary value of excess demand (or supply) for a single good or service. This is useful when analyzing individual market imbalances that contribute to the overall Walras' Law identity. It helps in understanding how price and excess demand interact to create market value.

Why it matters: Understanding the value of excess demand for individual markets is crucial for microeconomic analysis and for verifying Walras' Law in multi-market models. It highlights how market prices and quantities interact to determine market states, informing policy decisions related to market interventions and stability.

Symbols

Variables

$p_{i}$ = Price of Good i, $E_{i}$ = Excess Demand for Good i, $V_{i}$ = Value of Excess Demand

p_{i}

Price of Good i

E_{i}

Excess Demand for Good i

units

V_{i}

Value of Excess Demand

Walkthrough

Derivation

Formula: Walras' Law

Walras' Law states that the sum of the values of excess demands across all markets in an economy must be zero, given that all agents satisfy their budget constraints.

All economic agents (households, firms) satisfy their budget constraints, meaning the value of their purchases equals the value of their sales.
There are a finite number of markets (N) in the economy.
Prices for all goods are positive.

Define Individual Budget Constraints:

For each agent $j$ , the total value of their net trades (purchases $x_{ij}$ minus initial endowments $ω_{ij}$ ) across all $N$ markets must sum to zero. This means they spend exactly what they earn.

i = 1 \sum N p_{i} (x_{ij} - ω_{ij}) = 0

Aggregate Across All Agents:

Summing the individual budget constraints over all $M$ agents in the economy. Since each individual's budget constraint sums to zero, the sum of all individual budget constraints must also be zero.

j = 1 \sum M i = 1 \sum N p_{i} (x_{ij} - ω_{ij}) = 0

Rearrange and Define Excess Demand:

By changing the order of summation, we can group terms by market $i$ . The term $\sum_{j = 1}^{M} x_{ij}$ represents the total demand for good $i$ , and $\sum_{j = 1}^{M} ω_{ij}$ represents the total supply of good $i$ . The difference between total demand and total supply is the aggregate excess demand for good $i$ , denoted as $E_{i}$ .

i = 1 \sum N p_{i} (j = 1 \sum M x_{ij} - j = 1 \sum M ω_{ij}) = 0

Note: Thus, $E_{i} = \sum_{j = 1}^{M} x_{ij} - \sum_{j = 1}^{M} ω_{ij}$ .

Final Walras' Law Identity:

Substituting the definition of aggregate excess demand $E_{i}$ into the aggregated budget constraint yields Walras' Law: the sum of the values of excess demands across all markets is identically zero.

i = 1 \sum N p_{i} E_{i} = 0

Result

i = 1 \sum N p_{i} E_{i} = 0

Source: Mas-Colell, Whinston, Green - Microeconomic Theory, Chapter 17

Free formulas

Rearrangements

Solve for $p_{i}$

Walras' Law (Market Value): Make $p_{i}$ the subject

p_{i} = \frac{V _{i}}{E _{i}}

To make $p_{i}$ (Price of Good i) the subject of the market value component of Walras' Law, divide the value of excess demand ( $V_{i}$ ) by the excess demand ( $E_{i}$ ).

Difficulty: 1/5

Solve for $E_{i}$

Walras' Law (Market Value): Make $E_{i}$ the subject

E_{i} = \frac{V _{i}}{p _{i}}

To make $E_{i}$ (Excess Demand for Good i) the subject of the market value component of Walras' Law, divide the value of excess demand ( $V_{i}$ ) by the price ( $p_{i}$ ).

Difficulty: 1/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

Graph unavailable for this formula.

The graph is a straight line passing through the origin with a slope equal to E_i, meaning the value of excess demand increases at a steady, proportional rate as the price of the good grows. For an economics student, this linear relationship implies that small price values correspond to low excess demand, while large price values represent a significant market imbalance. The most important feature is that the constant slope means doubling the price of the good will exactly double the value of excess demand.

Graph type: linear

Why it behaves this way

Intuition

Imagine a balance sheet for a single market where the monetary value of the market's imbalance-whether a surplus of goods or a shortage-is calculated by multiplying the unit price by the net quantity difference the compared quantities.

V_{i}

The total monetary value representing the difference between the quantity demanded and the quantity supplied in market i.

A positive

V_{i}

means buyers collectively want to spend more on good i than sellers are offering at the current price, indicating a market shortage.

p_{i}

The prevailing market price per unit of good i.

This acts as the conversion factor, translating the quantity of excess demand (or supply) into its equivalent monetary value. A higher price amplifies the monetary impact of any given quantity imbalance.

E_{i}

The net quantity difference between the amount of good i demanded by consumers and the amount supplied by producers at the current price.

If positive, there is a shortage (demand > supply). If negative, there is a surplus (supply > demand). This term quantifies the extent of the market imbalance in terms of units of the good.

Free study cues

Insight

Canonical usage

This equation is used to calculate a monetary value, where price is expressed in currency per unit and excess demand in units, resulting in a value in currency.

Common confusion

Students may forget to ensure that the 'unit' in the price (e.g., USD/kg) matches the 'unit' of the excess demand (e.g., kg), leading to incorrect dimensional cancellation.

Unit systems

$V_{i}$ Currency - Represents the total monetary value of excess demand or supply for market i.

$p_{i}$ Currency/Unit - Price per unit of the good or service in market i.

$E_{i}$ Unit - The amount of excess demand (positive) or excess supply (negative) in market i.

One free problem

Practice Problem

In the market for good X, the price ( $p_{X}$ ) is $25 p er u ni t, an d t h ee x cess d e man d ($ $E_{X}$ $) i s 150 u ni t s . C a l c u l a t e t h e v a l u eo f e x cess d e man d ($ $V_{X}$ $) for good X.

Price of Good i25 $

Excess Demand for Good i150 units

Solve for: result

Hint: Multiply price by excess demand.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Assessing the monetary value of unsold inventory (excess supply) or unmet orders (excess demand) in a specific product market.

Study smarter

Tips

Ensure $p_{i}$ (price) is positive, as prices are typically non-negative.
A positive $E_{i}$ indicates excess demand, while a negative $E_{i}$ indicates excess supply.
The value $p_{i} E_{i}$ represents the monetary value of the imbalance in market $i$ .
Remember that Walras' Law applies to the *sum* of these values across all markets.

Avoid these traps

Common Mistakes

Confusing excess demand ( $E_{i}$ ) with total demand or total supply.
Incorrectly interpreting a negative value of $p_{i} E_{i}$ as excess demand (it means excess supply).

Common questions

Frequently Asked Questions

Walras' Law states that the sum of the values of excess demands across all markets in an economy must be zero, given that all agents satisfy their budget constraints.

Use this to calculate the monetary value of excess demand (or supply) for a single good or service. This is useful when analyzing individual market imbalances that contribute to the overall Walras' Law identity. It helps in understanding how price and excess demand interact to create market value.

Understanding the value of excess demand for individual markets is crucial for microeconomic analysis and for verifying Walras' Law in multi-market models. It highlights how market prices and quantities interact to determine market states, informing policy decisions related to market interventions and stability.

Confusing excess demand ($E_i$) with total demand or total supply. Incorrectly interpreting a negative value of $p_i E_i$ as excess demand (it means excess supply).

Assessing the monetary value of unsold inventory (excess supply) or unmet orders (excess demand) in a specific product market.

Ensure $p_i$ (price) is positive, as prices are typically non-negative. A positive $E_i$ indicates excess demand, while a negative $E_i$ indicates excess supply. The value $p_i E_i$ represents the monetary value of the imbalance in market $i$. Remember that Walras' Law applies to the *sum* of these values across all markets.

References

Sources

Wikipedia: Walras's law
Microeconomic Theory by Mas-Colell, Whinston, and Green
Hal Varian, Microeconomic Analysis
N. Gregory Mankiw, Principles of Economics
Mas-Colell, Andreu, Michael D. Whinston, and Jerry R. Green. Microeconomic Theory. Oxford University Press, 1995.
Mas-Colell, Whinston, Green - Microeconomic Theory, Chapter 17

Walras' Law (Market Value)

Overview

Variables

Derivation

Define Individual Budget Constraints:

Aggregate Across All Agents:

Rearrange and Define Excess Demand:

Final Walras' Law Identity:

Rearrangements

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

AK Growth Model

Frequently Asked Questions

Sources