Econ 201
Essential Mathematical Tools
Economics as a Marginalist Paradigm
Marginal Costs
– What do we mean by marginal costs?
• incremental, or additional, costs of producing one
more unit of output
– Difference in total costs of producing one more unit
– Marginal cost of the 4th unit = Total Costs of the 4th unit minus
the Total Costs of the 3rd unit
MC[4] = TC[4] – TC[3]
A Numeric Example
• From Alchian and Allen
# Tees produced
daily
Total Costs
0
$1.00
1
$1.90
2
$2.70
3
$3.40
4
$4.00
5
$4.70
6
$5.50
7
$6.40
8
$7.40
9
$8.60
Marginal Costs
A Numeric Example
• What Are the Marginal Costs
# Tees produced
daily
Total Costs
Marginal Costs
0
$1.00
---
1
$1.90
$0.90
2
$2.70
$0.80
3
$3.40
$0.70
4
$4.00
$0.60
5
$4.70
$0.70
6
$5.50
$0.80
7
$6.40
$0.90
8
$7.40
$1.00
9
$8.60
$1.20
All of the Numbers
# tees/day
Total Cost
Marg Cost
Total Rev
Marg Rev
Profit
Marg Profit
0
$1.00
$1.00
$0.00
$0.00
-$1.00
-$1.00
1
$1.50
$0.50
$1.00
$1.00
-$0.50
$0.50
2
$2.70
$1.20
$2.00
$1.00
-$0.70
-$0.20
3
$3.40
$0.70
$3.00
$1.00
-$0.40
$0.30
4
$4.00
$0.60
$4.00
$1.00
$0.00
$0.40
5
$4.70
$0.70
$5.00
$1.00
$0.30
$0.30
6
$5.50
$0.80
$6.00
$1.00
$0.50
$0.20
7
$6.40
$0.90
$7.00
$1.00
$0.60
$0.10
8
$7.40
$1.00
$8.00
$1.00
$0.60
$0.00
9
$8.60
$1.20
$9.00
$1.00
$0.40
-$0.20
What Do They Mean?
Marginal and Total
Costs increasing at
Increasing rate
Total and Marginal Costs
Total and Marginal Costs
Cost in Dollars
$10.00
$8.00
$6.00
$4.00
$2.00
$0.00
0
Total Cos t
Marg Cos t
1
2
3
4
5
6
# of Tees per day
7
8
9
Marginal Costs at
Minimum, TC
increasing at dec rate
What’s It Mean to a Supplier?
• Firm’s supply decision
– Supply up to the point where p >= MC
• Profit maximizing point
Profit Max
Dollars
Profits, Marginal Revenues & Costs
$1.40
$1.20
$1.00
$0.80
$0.60
$0.40
$0.20
$0.00
MR = MC
$1.00
$0.50
$0.00
-$0.50
-$1.00
-$1.50
0
1
2
3
4
5
6
# tees per day
7
8
9
Marg Rev
Marg Cost
Profit
From the Demand Side
• First Law of Demand
– What Does Law Of Demand Mean?
– all other factors being equal, as the price of
a good or service increases, consumer
demand for the good will decrease and vice
versa.
• Investopedia explains Law Of
Demand...
– summarizes the effect price changes on
consumer behavior. For example, a
consumer will purchase more pizzas if the
price of pizza falls. The opposite is true if
the price of pizza increases.
– http://www.investopedia.com/terms/l/lawo
fdemand.asp
A Demand Example
Price
Individual's Demand Curve
Qty Demanded
$10.00
1
$9.00
2
$8.00
3
$7.00
4
$6.00
5
$5.00
6
$4.00
7
$3.00
8
$2.00
9
$1.00
10
Price per unit
$12.00
$10.00
$8.00
$6.00
Price
$4.00
$2.00
$0.00
1
2
3
4
5
6
7
Quantity Demanded
8
9
10
Consumer’s Marginal Value
• Some basic definitions
– Total Willingness-to-pay: “value in use”
• How much would you be willing to pay for x units of the good than
go entirely without?
– Equals the area under the demand curve up to x units
Individual's Demand Curve
WTP for 4 units
Price per unit
$12.00
$10.00
$8.00
$6.00
Price
$4.00
$2.00
$0.00
1
2
3
4
5
6
7
Quantity Demanded
8
9
10
Computing Marginal Value
Price
Qty Demanded
$10.00
1
$9.00
2
$8.00
3
$7.00
4
$6.00
5
$5.00
6
$4.00
7
$3.00
8
$2.00
9
$1.00
10
Total and Marginal Value
Price
Qty Demanded
Amt Paid
Marginal Value
Total Value
Price x Qty Dem
$10.00
1
$10.00
$10.00
$10.00
$9.00
2
$18.00
$9.00
$19.00
$8.00
3
$24.00
$8.00
$27.00
$7.00
4
$28.00
$7.00
$34.00
$6.00
5
$30.00
$6.00
$40.00
$5.00
6
$30.00
$5.00
$45.00
$4.00
7
$28.00
$4.00
$49.00
$3.00
8
$24.00
$3.00
$52.00
$2.00
9
$18.00
$2.00
$54.00
$1.00
10
$10.00
$1.00
$55.00
Area under Demand
Difference in
TV(3)-TV(2)
MV is also equal
to price paid
In Graphic Terms
Note: (again) price = marginal value
Consumer is willing to buy up to P = MV
Dollars
Price, Total & Marginal Use Value
$12.00
$10.00
$8.00
$60.00
$50.00
$40.00
$6.00
$4.00
$2.00
$0.00
$30.00
$20.00
$10.00
$0.00
1
2
3
4
5
6
7
8
Quantity Demanded
9 10
Price
Marginal Value
Total Value
What Have We Learned?
• How to compute marginal or incremental
values
– Marginal cost: the additional (change in Tot Costs)
of producing one more unit
– Marginal value: the value to a consumer of
purchasing one more unit
The Bigger Lesson
• Sell rule for firms
– Firms will supply up to the point where the MC of
producing the next unit are just equal to the price it
receives for the good
• First law of supply: supply curves will be upward sloping
• Buy rule for consumers
– Consumers will buy up to the point that price equals MV
• First law of demand: demand curves are downward sloping
• Negative slope  diminishing marginal value of consuming next
unit