Efficiency and Equity: Resource Allocation, Surplus, and Market Efficiency

Chapter 5 – Efficiency and Equity

Resource Allocation Methods

Because resources are scarce, societies must decide how to allocate them among competing uses. Several methods exist for resource allocation, each with its own advantages and limitations.

• Market Price: Resources go to those willing and able to pay the market price. Example: Diamonds are allocated to those who can afford them.

• Command System: Allocation is determined by authority figures. Example: Workplace supervisors assign tasks to employees.

• Majority Rule: Resources are allocated according to the preferences of the majority. Example: Town Hall meetings decide on the use of local tax revenues.

• Contest: Winners receive the resource, often used when effort is hard to measure directly. Example: Employee bonus prizes.

• First Come, First Served: Resources go to those who arrive first. Example: Allocation of parking spots.

• Lottery: Resources are allocated randomly. Example: The USA Visa Lottery for Green Cards.

• Personal Characteristics: Allocation based on attributes such as age, gender, or other traits.

• Force: Resources are taken or allocated by force.

Note: In microeconomics, the focus is primarily on allocation by market price.

Allocative Efficiency

Allocative efficiency occurs when resources are used where they are most highly valued. This is achieved when the marginal benefit (MB) equals the marginal cost (MC):

$MB = MC$

At this point, the value to consumers of the last unit produced equals the opportunity cost to producers.

Demand and Marginal Benefit (MB)

Marginal Benefit and the Demand Curve

The marginal benefit (MB) of a good or service is the value of one more unit to a consumer. It is measured by the maximum price a consumer is willing to pay for an additional unit. The demand curve reflects this willingness to pay, so:

• The demand curve is also the marginal benefit curve.

Example: Jane's demand for ice-cream is given by $Q_d = -2P + 6$ or $P = -0.5Q_d + 3$. The marginal benefit of the 2nd unit is:

$MB = -2 \times 2 + 6 = 2$

This means Jane values the 2nd unit at $2, which is the highest price she is willing to pay for it.

Market Demand and Marginal Social Benefit (MSB)

• Market demand is the horizontal sum of all individual demand curves.

• The market demand curve represents the marginal social benefit (MSB) to society.

Consumer Surplus

When consumers pay less than what they are willing to pay, they receive a consumer surplus.

• Definition: Consumer surplus is the value (MB) of a good minus the price paid, summed over all units bought.

• It is measured by the area under the demand curve and above the price, up to the quantity bought.

Formula:

$CS = \sum (MB - P)$

Example: Market demand for ice-cream: $Q_d = -2P + 18$. If market price $P = 4$:

• Find $Q$: $Q = -2 \times 4 + 18 = 10$

• Consumer surplus is the area under the demand curve and above $P=4$ up to $Q=10$.

• For a linear demand curve, $CS = \frac{1}{2} \times base \times height$

Note: Do not confuse consumer surplus with a market surplus (when $Q_d < Q_s$).

Supply and Marginal Cost (MC)

Marginal Cost and the Supply Curve

The marginal cost (MC) is the cost of producing one more unit. It is measured by the minimum price a producer must receive to supply an additional unit. The supply curve reflects this minimum supply price, so:

• The supply curve is also the marginal cost curve.

Example: Mark's supply for ice-cream: $Q_s = 2P - 2$ or $P = 0.5Q_s + 1$. The marginal cost of the 2nd unit is:

$MC = 0.5 \times 2 + 1 = 2$

This means Mark is willing to supply the 2nd unit at a minimum price of $2.

Market Supply and Marginal Social Cost (MSC)

• Market supply is the horizontal sum of all individual supply curves.

• The market supply curve represents the marginal social cost (MSC) to society.

Producer Surplus

When producers receive a price higher than their marginal cost, they earn a producer surplus.

• Definition: Producer surplus is the price received minus marginal cost, summed over all units sold.

• It is measured by the area above the supply curve and below the market price, up to the quantity sold.

Formula:

$PS = \sum (P - MC)$

Example: Market supply for ice-cream: $Q_s = 2P - 6$. If market price $P = 6$:

• Find $Q$: $Q = 2 \times 6 - 6 = 6$

• Producer surplus is the area above the supply curve and below $P=6$ up to $Q=6$.

• For a linear supply curve, $PS = \frac{1}{2} \times base \times height$

Note: Do not confuse producer surplus with a market surplus (when $Q_d < Q_s$).

Market Efficiency

Market Equilibrium and Allocative Efficiency

The competitive market equilibrium is where quantity demanded equals quantity supplied ($Q_d = Q_s$). At this point, the marginal social benefit equals the marginal social cost ($MSB = MSC$), and total surplus is maximized.

Example: Suppose market demand and supply for ice-cream are:

• $Q_d = -2P + 18$

• $Q_s = 2P - 6$

Set $Q_d = Q_s$ to find equilibrium price and quantity:

$-2P + 18 = 2P - 6$

$18 + 6 = 2P + 2P$

$24 = 4P$

$P^* = 6$

Plug $P^*$ into either equation to find $Q^*$:

$Q^* = -2 \times 6 + 18 = 6$

At $Q^* = 6$, $P^* = 6$.

Marginal Analysis at Different Quantities

• If $Q < Q^*$: $MSB > MSC$ → Increase $Q$ to improve efficiency.

• If $Q > Q^*$: $MSB < MSC$ → Decrease $Q$ to improve efficiency.

• At $Q^*$: $MSB = MSC$ → Allocative efficiency is achieved.

Consumer and Producer Surplus at Equilibrium

• Consumer Surplus: $CS = \frac{1}{2} (18 - 6) \times 6 = 36$

• Producer Surplus: $PS = \frac{1}{2} (6 - 3) \times 6 = 9$

• Total Surplus: $CS + PS = 36 + 9 = 45$

Total surplus is maximized at equilibrium, indicating market efficiency.

Summary Table: Key Concepts

Concept	Definition	Graphical Area
Consumer Surplus	Value (MB) minus price paid, summed over all units bought	Area under demand curve and above price
Producer Surplus	Price received minus marginal cost, summed over all units sold	Area above supply curve and below price
Total Surplus	Sum of consumer and producer surplus	Area between demand and supply curves up to equilibrium quantity

Key Properties of Market Equilibrium

• Allocative efficiency is achieved ($MB = MC$ or $MSB = MSC$).

• Quantity demanded equals quantity supplied ($Q_d = Q_s$).

• Total surplus (consumer + producer surplus) is maximized.

Additional info: In real-world markets, factors such as externalities, public goods, and market power can prevent markets from achieving allocative efficiency. These topics are covered in later chapters.