5. The demand function of a good is P = 80 - 0.20 a) What are the slope and intercept? Interpret them. b) What quantity of the good will be demanded at the price P-45? c) At what price will the demand be 60? d) Graph the demand function P = 80 -0.2Q. e) Express the demand function in the form Q = f(P). Graph it.
Answers
SOLUTION
TO DETERMINE
The demand function of a good is P = 80 - 0.20Q
a) What are the slope and intercept? Interpret them.
b) What quantity of the good will be demanded at the price P 45?
c) At what price will the demand be 60?
d) Graph the demand function P = 80 -0.2Q.
e) Express the demand function in the form Q = f(P). Graph it.
EVALUATION
Here it is given that the demand function of a good is P = 80 - 0.20Q
a) The demand function is
P = 80 - 0.20Q - - - - - - - (1)
Which can be rewritten as
P = - 0.20Q + 80
Which is of the slope intercept form
y = mx + c
Slope = - 0.20
Intercept = 80
b) The price is P = 45
From Equation 1 we get
45 = 80 - 0.20Q
⇒ 0.20Q = 35
⇒ Q = 175
The quantity of the good will be demanded at the price P 45 is 175
c) When demand is 60
Q = 60
P = 80 - 0.20Q gives
P = 80 - ( 0.20 × 60 )
⇒ P = 80 - 12
⇒ P = 68
The price will be 68 when the demand is 60
d) The demand function is P = 80 - 0.20Q
Graph : Graph is referred to the attachment
e) The demand function is
P = 80 - 0.20Q
⇒ 0.20Q = 80 - P
⇒ Q = 400 - 5P
Which is of the form Q = f(P)
Graph : Graph is referred to the attachment
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