Using Marginal Analysis in Economics
Introduction
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Provenance: wkimedia
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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 (Astart) from the ending value of the first variable (Aend) to get the change (ΔA).
- Subtract the starting value of the second variable (Bstart) from the ending value of the second variable (Bend) 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 (TCstart) from the ending value of the Total Cost (TCend) to get the change in Total Cost (ΔTC).
- Subtract the starting value of the Quantity (Qstart) from the ending value of the Quantity (Qend) 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 (taxstart) from the ending value of total tax (taxend) to get the change in total tax (∆tax).
- Subtract the starting value of the income (incomestart) from the ending value of the income (incomeend) 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:
The table presents revenue and cost information for Happily Ever After, a small bakery specializing in wedding cakes. How many cakes per day should Happily Ever After produce in order to maximizes its profit?
Looking at the table, we can see that Happily Ever After will make a $100 profit by producing and selling the first cake. That's where we'll start.
Should Happily Ever After produce and sell a second cake?
From the table, we see that the marginal revenue (also called marginal benefit) of the second cake is $25. This means that producing and selling the second cake will increase total revenue by $25.
Total Revenue (TR) increases from $150 to $175 from 1 to 2 cakes. The Marginal Revenue (MR) of the second cake is therefore:
- ∆TR = $175 - $150 = $25
- ∆Q = 2 – 1 = 1
- MR = $25 ÷ 1 = $25
Though the marginal revenue increases by $25, we also see an increased cost with the production of a second cake. Looking at the table, we see the marginal cost of the second cake is $20. This means that producing and selling the second cake will increase total cost by $20.
Total Cost (TC) increases from $50 to $70 from 1 to 2 cakes. The Marginal Cost (MC) of the second cake is therefore:
- ∆TC = $70 - $50 = $20
- ∆Q = 2 – 1 = 1
- MC = $20 ÷ 1 = $20
The marginal revenue from the second cake ($25) is greater than its marginal cost ($20). Therefore, Happily Ever After should produce and sell a second cake per day.
So we can see that Happily Ever After will make a $105 profit by producing and selling the second cake.
Should Happily Ever After produce and sell a third cake?
We see from the table that the marginal revenue of the third cake is $20. This means that producing and selling the third cake will increase total revenue by $20.
Total Revenue (TR) increases from $175 to $185 from 2 to 3 cakes. The marginal Revenue (MR) of the third cake is therefore:
- ∆TR = $195 - $175 = $20
- ∆Q = 3 – 2 = 1
- MR = $20 ÷ 1 = $20
Though the marginal revenue increases by $20, we again see a further-increased cost with the production of a third cake. Looking at the table, we see the marginal cost of the third cake is $30. This means that producing and selling the third cake will increase total costs by $30.
Total Cost (TC) increases from $70 to $100 from 2 to 3 cakes. The Marginal Cost of the third cake is therefore:
- ∆TC = $100 - $70 = $30
- ∆Q = 3 – 2 = 1
- MC = $30 ÷ 1 = $30
The marginal benefit of the third cake ($20) is less than its marginal cost ($30). Therefore, Happily Ever After should not produce and sell a third cake per day.
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:
The marginal propensities to save and consume are key concepts in Keynesian macroeconomics. The marginal propensity to save is the additional saving that results from an additional dollar of disposable income; the marginal propensity to consume is the additional consumption expenditure that results from an additional dollar of disposable income.
Consider the following table on disposable income, consumption and savings.
Provenance: Michelle Sheran, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Studying the table, we can determine that the marginal propensity to save is 0.25. That means that a household will save 25 cents of each additional dollar of disposable income.
To calculate MPS:
- Subtract the starting value of savings from the ending value of saving to get the change in saving.
- ∆Saving = $900 - $750 = $150
- Subtract the starting value of the disposable income from the ending value of disposable income to get the change in disposable income.
- ∆Income = $1000 - $800 = $200
- Divide the change in saving by the change in disposable income to get the marginal propensity to save (MPS).
- MPS = ∆Saving ÷ ∆Income = $150 ÷ $200 = 0.25
The marginal propensity to consume in this example is 0.75. That means that a household will spend 75 cents of each additional dollar of disposable income.
To calculate MPC:
- Subtract the starting value of consumption expenditure from the ending value of consumption expenditure to get the change in consumption.
- ∆Consumption = $100 - $50 = $50
- Subtract the starting value of the disposable income from the ending value of disposable income to get the change in disposable income.
- ∆Income = $1000 - $800 = $200
- Divide the change in consumption by the change in disposable income to get the marginal propensity to consume (MPC).
- MPC = ∆Consumption ÷ ∆Income = $50 ÷ $200 = 0.75
✓ 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.
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