Lectures in Microeconomics-Charles W. Upton The Mathematics of Demand Functions D P Q
Lectures in Microeconomics-Charles W. Upton The Mathematics of Demand Functions.
Dec 22, 2015
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Lectures in Microeconomics-Charles W. Upton
The Mathematics of Demand Functions
D
P
Q
The Mathematics of Demand Functions
Demand Functions In Different Forms
• Graphs of quantity demanded against price
D
P
Q
The Mathematics of Demand Functions
Demand Functions In Different Forms
• Graphs of quantity demanded against price– They need not be
straight lines
D
P
Q
The Mathematics of Demand Functions
Demand Functions In Different Forms
• Tables Price Quantity
$0.40 100
$0.50 90
$0.60 80
The Mathematics of Demand Functions
Demand Functions In Different Forms
• Mathematical equations
Q=100-2P
The Mathematics of Demand Functions
Demand Functions In Different Forms
• Mathematical equations– Linear or Non
Linear
Q=100-2P
Q=10P-2
The Mathematics of Demand Functions
Indirect demand functions
• Gives price as a function of quantity, not the other way around.
• We can always restate indirect demand functions as direct demand functions and vice versa.
The Mathematics of Demand Functions
A Graphical Interpretation
• Knowing price we know quantity demanded.
D
P
Q
The Mathematics of Demand Functions
A Graphical Interpretation
• It also works the other way.
D
P
Q
The Mathematics of Demand Functions
Ditto with Tables
Price Quantity
$0.40 100
$0.50 90
$0.60 80
The Mathematics of Demand Functions
An Example
Q = 100 – 2P
The Mathematics of Demand Functions
An Example
Q = 100 – 2P
2P + Q = 100 – 2P +2P
The Mathematics of Demand Functions
An Example
Q = 100 – 2P
2P + Q = 100 – 2P +2P
2P + Q = 100
The Mathematics of Demand Functions
An Example
2P + Q = 100
2P + Q – Q = 100 – Q
2P = 100 – Q
The Mathematics of Demand Functions
An Example
2P = 100 – Q
(1/2)[2P] = (1/2)[100-Q]
P = 50 – (1/2)Q
The Mathematics of Demand Functions
A Second Example
P = 50 – (1/2)Q
The Mathematics of Demand Functions
A Second Example
P = 50 – (1/2)Q
2P = 2[50-(1/2)Q]
2P = 100 – Q
The Mathematics of Demand Functions
A Second Example
2P = 100 – Q
Q + 2P = 100 – Q + Q
Q + 2P = 100
The Mathematics of Demand Functions
A Second Example
Q + 2P = 100 – Q + Q
Q + 2P = 100
Q + 2P – 2P = 100 –2P
Q = 100 – 2P
The Mathematics of Demand Functions
Some Assignments
P = 12 – 3Q
Q = 100 – 10P
The Mathematics of Demand Functions
Some Assignments
P = 12 – 3Q
Q = 100 – 10P
Q = 4 – (1/3)P
P = 10 – 0.1Q
The Mathematics of Demand Functions
End
©2004 Charles W. Upton
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