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The Mathematics of demand functions
1. The Mathematics of Demand Functions
PThe Mathematics of Demand
Functions
D
Q
Lectures in Microeconomics-Charles W. Upton
2. Demand Functions In Different Forms
• Graphs ofquantity
demanded against
price
P
D
Q
The Mathematics of
3. Demand Functions In Different Forms
• Graphs ofquantity
demanded against
price
P
– They need not be
straight lines
D
Q
The Mathematics of
4. Demand Functions In Different Forms
• TablesPrice
Quantity
$0.40
100
$0.50
90
$0.60
80
The Mathematics of
5. Demand Functions In Different Forms
• Mathematicalequations
Q=100-2P
The Mathematics of
6. Demand Functions In Different Forms
• Mathematicalequations
– Linear or Non
Linear
Q=100-2P
Q=10P-2
The Mathematics of
7. Indirect demand functions
• Gives price as a function of quantity, not theother way around.
• We can always restate indirect demand
functions as direct demand functions and
vice versa.
The Mathematics of
8. A Graphical Interpretation
• Knowing pricewe know quantity
demanded.
P
D
Q
The Mathematics of
9. A Graphical Interpretation
• It also works theother way.
P
D
Q
The Mathematics of
10. Ditto with Tables
PriceQuantity
$0.40
100
$0.50
90
$0.60
80
The Mathematics of
11. An Example
Q = 100 – 2PThe Mathematics of
12. An Example
Q = 100 – 2P2P + Q = 100 – 2P +2P
The Mathematics of
13. An Example
Q = 100 – 2P2P + Q = 100 – 2P +2P
2P + Q = 100
The Mathematics of
14. An Example
2P + Q = 1002P + Q – Q = 100 – Q
2P = 100 – Q
The Mathematics of
15. An Example
2P = 100 – Q(1/2)[2P] = (1/2)[100-Q]
P = 50 – (1/2)Q
The Mathematics of
16. A Second Example
P = 50 – (1/2)QThe Mathematics of
17. A Second Example
P = 50 – (1/2)Q2P = 2[50-(1/2)Q]
2P = 100 – Q
The Mathematics of
18. A Second Example
2P = 100 – QQ + 2P = 100 – Q + Q
Q + 2P = 100
The Mathematics of
19. A Second Example
Q + 2P = 100 – Q + QQ + 2P = 100
Q + 2P – 2P = 100 –2P
Q = 100 – 2P
The Mathematics of
20. Some Assignments
P = 12 – 3QQ = 100 – 10P
The Mathematics of
21. Some Assignments
P = 12 – 3QQ = 4 – (1/3)P
Q = 100 – 10P
P = 10 – 0.1Q
The Mathematics of
22. End
©2004 CharlesW. Upton
The Mathematics of