# 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.

- Subtract the starting value of the first variable (A
_{start}) from the ending value of the first variable (A_{end}) to get the change (ΔA). - Subtract the starting value of the second variable (B
_{start}) from the ending value of the second variable (B_{end}) to get the change (ΔB). - 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).

- Subtract the starting value of Total Cost (TC
_{start}) from the ending value of the Total Cost (TC_{end}) to get the change in Total Cost (ΔTC). - Subtract the starting value of the Quantity (Q
_{start}) from the ending value of the Quantity (Q_{end}) to get the change in Quantity (ΔQ). - 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.

- Subtract the starting value of total tax (tax
_{start}) from the ending value of total tax (tax_{end}) to get the change in total tax (∆tax). - Subtract the starting value of the income (income
_{start}) from the ending value of the income (income_{end}) to get the change in income (∆income). - 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.