Demand Equations
Onsite Session
September 20, 2023
Three types of demand relations
2
1
General Demand Function
2
Direct Demand Functions
Qd = f(P)
1
Inverse Demand Functions
P = f(Qd)
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Qd = f ( P, M , PR , , Pe , N )
1
General Demand Function
Six variables that influence Qd
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•
•
•
•
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Price of a good or service (P)
Incomes of consumers (M)
Prices of related goods & services (PR)
Taste patters of consumers (T)
Expected future price of a produce (Pe)
Number of consumers in market (N)
•
3
Qd = f ( P, M , PR , , Pe , N )
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General Demand Function
Qd = a + bP + cM + dPR + e  + fPe + gN
 Slope parameters are b, c, d, e, f, and g.
 Measure effect on Qd of changing one of the variables while holding the others constant
 Sign of parameter shows how variable is related to Qd
• Positive sign indicates direct relationship
• Negative sign indicates inverse relationship
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General Demand Function
Qd = a + bP + cM + dPR + e  + fPe + gN
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Direct Demand Function
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 The direct demand function, or simply demand, shows how quantity
demanded, Qd , is related to product price, P, when all other variables are held
constant.
 Law of Demand
 Qd increases when P falls & Qd decreases when P rises, all else constant

∆𝑄𝑑
∆𝑃
must be negative
Qd = f(P)
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Direct Demand Function
 A direct demand function is obtained by holding all the variables in the general
demand function constant except price.
For example, using a three-variable demand function, where the bar over the variables M and P means that
those variables are held constant.
ഥ 𝑷𝒓 = 𝒇(𝑷)
𝑸𝒅 = 𝒇 𝑷, 𝑴,
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3
Inverse Demand Function
 Traditionally, price (P) is plotted on the vertical axis & quantity demanded
(Qd) is plotted on the horizontal axis
 The equation plotted is the inverse demand function.
P= f(Qd)
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THREE DEMAND SCHEDULES
𝑄𝑑 = 3,200 − 10𝑃 + 0.05𝑀 − 24𝑃𝑅
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M = $60,000; PR=$200
M = $64,000; PR=$200
M = $52,000; PR=$200
𝑄𝑑 = 1,400 − 10𝑃
𝑄𝑑 = 1,600 − 10𝑃
𝑄𝑑 = 1,000 − 10𝑃
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THREE DEMAND SCHEDULES
𝑄𝑑 = 3,200 − 10𝑃 + 0.05𝑀 − 24𝑃𝑅
Demand
Equations
10
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D0: Qd = 1400 - 10P
Price
M = $60,000; PR=$200
$140
$120
$100
$80
$60
$40
$20
0
200
400
600
800
1000
1200
D1: Qd = 1600 - 10P
D2: Qd = 1000 - 10P
M = $64,000; PR=$200 M = $52,000; PR=$200
200
400
600
800
1000
1200
1400
0
0
0
200
400
600
800
THREE DEMAND SCHEDULES
Demand
Equations
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D0: Qd = 1400 - 10P D1: Qd = 1600 - 10P D2: Qd = 1000 - 10P
Price
M = $60,000; PR=$200
M = $64,000; PR=$200
M = $52,000; PR=$200
$140
0
200
0
$120
200
400
0
$100
400
600
0
$80
600
800
200
$60
800
1000
400
$40
1000
1200
600
$20
1200
1400
800
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DEMAND EQUATIONS – LEARNING BY DOING!
Consider the general demand function:
𝑄𝑑 = 8,000 − 16𝑃 + 0.5𝑀 − 20𝑃𝑅
a.
b.
c.
d.
e.
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Derive the equation for the demand function when M = $30,000 and PR=$50
Interpret the intercept and slope parameters of the demand function derived in part a.
Sketch a graph of the demand function in part a. Where does the demand function intersect the quantitydemanded axis? Where does it intersect the price axis?
Using the demand function from part a, calculate the quantity demanded when the price of the good is $1,000 and
when the price is $500.
Derive the inverse of the demand function in part a. Using the inverse demand function, calculate the demand
price for 15,000 units of the good.
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THANK YOU!