Lecture 3: Diminishing Marginal Returns, Indifference Curves, and Marginal Rate of Substitution

Learning Goals

By the end of class, you should be able to:

• Define the law of diminishing marginal returns and explain its implications
• Define scarcity and distinguish it from shortage
• Model how individuals make choices under scarcity to maximize well-being (utility)
• Graph indifference curves and interpret the marginal rate of substitution (MRS)

Cold Open: The Airplanes Experiment

You are part of a firm whose goal is simple:

Produce as many valid, labeled paper airplanes as possible within each round.

Some things you can change:

• How you organize labor
• Who folds, who labels, who fetches paper

Some things you cannot change:

• Time per round
• Number of workers in your firm
• Number of markers

What You’re Learning

This experiment is designed to help you experience:

• How production works with limited resources
• What happens when some inputs are fixed
• Why adding more workers doesn’t always help

We’ll name the economics after you see it.

Product Definition (Quality Matters)

A paper airplane counts as valid output only if it:

• Matches the approved folding design
• Has the firm’s label written clearly (e.g. “XYZ Airlines”)
• Is fully completed before time is called

❌ Incomplete or unlabeled planes do not count.

Quality inspectors have final authority.

Approved Folding Design

All planes must match this design.

Do not experiment with new designs.

This keeps the focus on production, not creativity.

Fixed and Variable Inputs (Implicit Rules)

• Labor (workers): variable
• Markers: fixed (one per firm)
• Time: fixed
• Paper: unlimited, but costly to collect

You may discover why this matters.

Paper Distribution Rule

We will use the warehouse system:

• A paper distributor stands at the front
• A firm may send as many workers as it wants
• Each worker may collect only ONE sheet per trip

You must decide how to allocate workers between:

• Folding
• Labeling
• Fetching paper

Round Structure

Recording the Data

Live results (in-class)

What to Pay Attention To

As the experiment runs, notice:

• Where workers get stuck waiting
• Whether adding workers helps or hurts
• What limits production

Don’t try to optimize perfectly — observe.

Discussion

Be ready to answer:

1. Did bigger firms produce more planes overall?
2. Did doubling workers double output?
3. Where did workers get in each other’s way?
4. What inputs were fixed in this experiment?

Why We Did This

This experiment illustrates a central economic idea:

Adding more of one input doesn’t help much when other inputs are fixed.

Next, we’ll connect this to scarcity, choice, and how people decide what to do with their time.

What Did You Notice?

• Did total output increase each round?
• Did output increase by the same amount each round?
• When did things start to slow down?

Law of Diminishing Marginal Returns

Definition:

Holding some inputs fixed, adding more of a variable input eventually increases output by less and less.

• Not about laziness
• Not about mistakes
• About constraints

From Production to Scarcity

Why does diminishing marginal returns happen?

• Some inputs are fixed
• Space, tools, attention, time

We cannot have unlimited amounts of everything we want.

Scarcity vs. Shortage

Scarcity

• Wants exceed available resources
• Universal and permanent

Shortage

• Quantity demanded > quantity supplied at a given price
• Institutional and temporary

Scarcity Forces Choice

• More of one thing means less of another
• Every choice has an opportunity cost

Economics studies how people make the best possible choices under constraints.

Modeling Choice Under Scarcity

Preferences and Indifference Curves

Marginal Rate of Substitution (MRS)

The Feasible Set

Constraints matter.

• You only have 24 hours in a day
• Your wage determines how much consumption one hour of work buys

Marginal Rate of Transformation (MRT)

Definition:

The marginal rate of transformation (MRT) is how much consumption you must give up to get one more unit of free time.

Making the Best Choice

Optimal choice occurs where:

MRS = MRT

What happens with extra income?

What if Karim gets a universal basic income of 100 euros per day? Then he has at least 1000 euros per year without working.

This moves his budget constraint outward and changes his optimal choice.

What If Wages Change?

Is the model we just went through any good?

History of working hours

In our model?

Consumption and free time per day in US from 1900 to 2020

By gender

Around the world, women do more “unpaid” work than men

Why is this the case? Let’s check the model…

Splitting domestic work and paid work

Consider Ana and Luis, a couple with:

• Two young children
• Similar preferences and skills
• Can both find employment at some wage and can work 8 hours maximum per day
• Need 14 hours of domestic work, including childcare, per day

How can they divide up domestic work and paid work to maximize their well-being?

The answer depends on differences in pay

Big Picture Summary

1. Scarcity is unavoidable
2. Scarcity creates tradeoffs
3. Tradeoffs are modeled with constraints and preferences
4. Optimal choices satisfy MRS = MRT

Looking Ahead

• Aggregating constrained choices gives demand curve, labor supply curves
• Firm production functions and supply curves
• Why people respond differently to the same price change