Price Elasticity, Consumer Equilibrium & Returns to Scale

Price Elasticity of Demand (PED)

Price Elasticity of Demand (PED) is an economic measure that shows how sensitive the quantity demanded of a good is to a change in its price. In simpler terms, it tells us how much consumers will reduce or increase their purchases when the price changes.

The law of demand states that price and quantity move in opposite directions, but elasticity measures the magnitude of that move.

Methods of Measuring Price Elasticity

While there are several ways to calculate this sensitivity, the two most prominent methods are the Percentage Method and the Total Outlay Method.

1. The Percentage Method (Flux Method)

Developed by Dr. Alfred Marshall, this is the most common mathematical approach. It calculates the ratio of the percentage change in demand to the percentage change in price.

The formula:

Where:

• ΔQ: Change in quantity (New – Old)
• ΔP: Change in price (New – Old)
• Q: Original quantity
• P: Original price

Interpretation

• Elastic (E_p > 1): If a 10% change in price leads to a 20% change in demand.
• Inelastic (E_p < 1): If a 10% change in price leads to only a 5% change in demand.
• Unitary (E_p = 1): If the percentage change in both is exactly the same.

2. The Total Outlay Method (Expenditure Method)

This method measures elasticity by looking at total spending (Total Outlay = Price × Quantity) of consumers before and after a price change. It does not give a specific numerical value but classifies demand into three categories.

How it works

• Elastic Demand: If you lower the price and total revenue increases, consumers reacted strongly to the discount.
• Inelastic Demand: If you lower the price and total revenue drops, consumers did not buy enough extra units to offset the lower price per unit.
• Unitary Demand: If you change the price and total spending stays exactly the same, the change in price was perfectly offset by the change in quantity.

Ordinal Utility Analysis and Consumer Equilibrium

In ordinal utility analysis — primarily associated with Hicks and Allen — consumer equilibrium is achieved using the indifference curve (IC) and the budget line. Unlike the cardinal approach, it assumes satisfaction cannot be measured in numbers but can be ranked in order of preference.

1. Conditions for Equilibrium

A consumer is in equilibrium when they maximize satisfaction given their income and the prices of goods. Two conditions must be met:

• Necessary Condition: The budget line must be tangent to the indifference curve. At this point, the slope of the IC (Marginal Rate of Substitution, MRS_xy) equals the slope of the budget line (price ratio, P_x/P_y).
• Sufficient Condition: The indifference curve must be convex to the origin at the point of equilibrium. This means MRS_xy must be diminishing.

2. Critical Examination

While the ordinal approach is considered more realistic than the cardinal one, it faces several critical challenges:

1. A. The “Old Wine in New Bottles” Critique

   Critics like Professor Robertson argue that the ordinal approach is simply the cardinal approach in disguise. To rank preferences as “higher” or “lower,” a consumer must have some underlying idea of the magnitude of utility, which brings the theory back to quantitative measurement.

2. B. Unrealistic Assumptions
   • Rationality: The theory assumes consumers are calculating agents who perfectly compare all combinations. In reality, consumers often buy impulsively or out of habit.
   • Divisibility of Goods: The model assumes goods can be bought in tiny fractions to reach the exact tangency point. However, many goods (like cars or refrigerators) are indivisible, making a perfect tangent equilibrium mathematically impossible in practice.
3. C. Ignoring the Endowment Effect

   The theory assumes a consumer’s indifference map is independent of current possessions. Behavioral economics suggests people value what they already own more than what they don’t (loss aversion), which can distort the shape of indifference curves.

4. D. Static Nature

   The analysis is a snapshot in time. It does not easily account for changes in tastes, the impact of advertising, or the introduction of new products, all of which constantly shift the consumer’s equilibrium point.

The Law of Returns to Scale

The law of returns to scale is a long-run production theory that explains how a firm’s output changes when all inputs (labor, capital, land, etc.) are increased simultaneously and in the same proportion. Unlike the short-run law of variable proportions, there are no fixed factors here; the entire scale of the business expands.

The Three Stages of Returns to Scale

When a firm increases all its inputs by a certain percentage (for example, 10%), the resulting output follows three distinct stages:

1. Increasing Returns to Scale (IRS)

In this stage, the percentage increase in output is greater than the percentage increase in inputs.

• Example: If you double all your inputs (100% increase), your output more than doubles (for example, a 150% increase).
• Significance: This indicates the firm is becoming more efficient as it grows.

2. Constant Returns to Scale (CRS)

In this stage, the percentage increase in output is exactly equal to the percentage increase in inputs.

• Example: Doubling your inputs leads to exactly a double in output.
• Significance: This is often called the ‘optimum capacity’ of the firm, where economies and diseconomies of scale balance each other out.

3. Decreasing Returns to Scale (DRS)

In this stage, the percentage increase in output is less than the percentage increase in inputs.

• Example: Doubling your inputs leads to only a 50% increase in output.
• Significance: This indicates the firm has become too large and unwieldy, leading to inefficiencies.

Causes of Application (Why It Happens)

The behavior of these returns is driven by economies of scale (advantages) and diseconomies of scale (disadvantages).

A. Causes of Increasing Returns (Economies)

• Specialization: As scale increases, labor can be divided into specialized tasks. A worker who repeats one task becomes faster and more skilled, boosting productivity.
• Indivisibility of Factors: Certain machines or management systems have a minimum size. You cannot buy ‘half’ of them. As production grows, these indivisible factors are utilized to their full capacity, lowering the cost per unit.
• Dimensional Relations: Sometimes doubling the physical size of a container more than doubles its volume. For example, doubling the radius of a pipe can increase flow by four times.
• Managerial Economies: Large firms can afford specialized managers (HR, marketing, finance) who handle their departments more efficiently than a single owner trying to do everything.

B. Causes of Decreasing Returns (Diseconomies)

• Complexity and Coordination: When a firm becomes a giant, communication between departments slows. It takes longer to make decisions, and red tape (bureaucracy) increases.
• Control Problems: Top management loses direct contact with workers on the factory floor, making it harder to monitor efficiency and maintain motivation.
• Exhaustion of Natural Resources: In industries like mining or agriculture, expanding the scale eventually forces the use of less productive land or deeper, more expensive mines.

Firm Equilibrium in Perfect Competition

A firm is said to be in equilibrium when it has no incentive to expand or contract its level of output. At this point, the firm is either maximizing total profits or minimizing total losses. In economic terms, this is a ‘state of rest’ where the firm has reached its most advantageous position given market conditions.

In a perfect competition market, the firm is a price taker. Since many firms sell identical products, the market price is determined by industry supply and demand, and the individual firm must accept this price. Consequently, the firm’s demand curve is perfectly elastic (horizontal), meaning P = Average Revenue (AR) = Marginal Revenue (MR).

1. Necessary Conditions for Equilibrium

To reach equilibrium, a firm must satisfy two specific conditions:

• First-Order Condition (Necessary): Marginal Revenue must equal Marginal Cost (MR = MC). Since P = MR in perfect competition, this is often written as P = MC.
• Second-Order Condition (Sufficient): The MC curve must cut the MR curve from below. This means that after the equilibrium point, marginal cost should be rising. If MC were falling, the firm could increase profit by producing more.

2. Short-Run Equilibrium

In the short run, the firm can face three different situations depending on its average cost (AC) relative to the market price:

• Supernormal Profits: Occurs when the market price is higher than average cost (P > AC).
• Normal Profits (Break-even): Occurs when the market price is exactly equal to average cost (P = AC). Here, the firm covers all costs, including the opportunity cost of the owner’s time.
• Minimum Losses: Occurs when price is lower than average cost (P < AC) but still above average variable cost (AVC). The firm continues to operate to cover part of its fixed costs.

The Shut-down Point: If price falls below average variable cost (P < AVC), the firm will stop production entirely to minimize losses, as it cannot even cover its day-to-day operating expenses.

3. Long-Run Equilibrium

In the long run, firms have enough time to enter or exit the industry.

• If firms are making supernormal profits, new firms will enter, increasing supply and driving the price down.
• If firms are making losses, some will exit, decreasing supply and driving the price up.

Therefore, in the long run, all firms in perfect competition earn only normal profits. The equilibrium occurs where:

This ensures ‘Productive Efficiency,’ as the firm is producing at the lowest possible average cost.