# Using Marginal Analysis in Economics

## Introduction

The margin is a small change that can be measured. Many everyday decisions are made using marginal analysis.

• Should I eat one more donut?
• Should I hit the snooze button again?
• Should I add another roommate to the lease?

Economic decisions often depend on the margin as well. By understanding the numbers, an economist can help make better-informed decisions as they go about their business.

• What is the change in cost as quantity produced changes (marginal cost)
• What is the change in revenue as quantity produced changes (marginal revenue)
• What is the change in tax paid as income changes (marginal tax rate)
• What is the change in savings as income changes (marginal savings rate)

## How do I calculate marginal change?

Marginal change is measured by dividing the change in one variable by the change in another variable.

1. Subtract the starting value of the first variable (Astart) from the ending value of the first variable (Aend) to get the change (ΔA).
2. Subtract the starting value of the second variable (Bstart) from the ending value of the second variable (Bend) to get the change (ΔB).
3. Divide the change in the first variable by the change in the second variable (ΔA/ΔB).

Shown another way:

A_"end" - A_"start" = \DeltaA
B_"end" - B_"start" = \DeltaB
marginal change = (\DeltaA)/(\DeltaB)

### Calculating marginal cost

Marginal Cost (MC) is the change in Total Cost (TC) divided by the change in Quantity (Q).

1. Subtract the starting value of Total Cost (TCstart) from the ending value of the Total Cost (TCend) to get the change in Total Cost (ΔTC).
2. Subtract the starting value of the Quantity (Qstart) from the ending value of the Quantity (Qend) to get the change in Quantity (ΔQ).
3. Divide the change in Total Cost by the change in the Quantity (ΔTC/ΔQ).

Shown another way:

TC_"end" - TC_"start" = \DeltaTC
Q_"end" - Q_"start" = \DeltaQ
marginal cost (MC) = (\DeltaTC)/(\DeltaQ)

### Calculating marginal tax rate

Marginal Tax Rate is the change in total tax divided by the change in income. The difference here is that marginal tax rates are expressed as a percentage, rather than a fraction.

1. Subtract the starting value of total tax (taxstart) from the ending value of total tax (taxend) to get the change in total tax (∆tax).
2. Subtract the starting value of the income (incomestart) from the ending value of the income (incomeend) to get the change in income (∆income).
3. Divide ∆tax by ∆income x 100 (to get a percentage)

Shown another way:

tax_"end" - tax_"start" = \Deltatax
\i\ncome_"end" - \i\ncome_"start" = \Delta\i\ncome
marginal tax rate = (\Deltatax)/(\Delta\i\ncome) xx 100%

## Where is marginal analysis used in Microeconomics?

Marginal analysis is useful for microeconomic decision-making:

• How much a firm should sell
• How much a consumer should buy
• How many workers an employer should hire

Let's look at a hypothetical example:

## Where is marginal analysis used in Macroeconomics?

Marginal analysis is often used in making policy decisions:

• How much should taxes be changed?
• How much will consumers spend if incomes change?
• How much will businesses invest if interest rates change?

Let's work through some new concepts:

### ✓ Final thoughts on the margin

Be sure to recognize the difference between marginals and averages. For example, consider average cost:

• Average Cost (AC) is the cost per unit of output and is calculated from total cost (TC) and quantity (Q) as AC = TC ÷ Q
• Average cost tells a firm how much each unit of its product costs on average. It's the total cost spread out over all units of output.

Contrast average cost with marginal cost:

• Marginal Cost (MC) is the cost of an additional unit of output and is calculated from the change in total cost (∆TC) and the change in quantity (∆Q) as MC = ∆TC ÷ ∆Q
• Marginal cost tells a firm how much it will cost to produce one more unit of its product. It's the additional cost of the next unit of output.