two points on a linear demand function are (2080000) and (3062500)
a) determine the demand function q=f(p)
b) determine what price would result in demand of 50000 units
c) interpret the slope of function
d) define the restricted domain and range for the function
e) sketch f(p)
Answers
Given : two points on a linear demand function are (20 , 80000) and (30 , 62500)
To Find : a) determine the demand function q=f(p)
b) determine what price would result in demand of 50000 units
c) interpret the slope of function
d) define the restricted domain and range for the function
e) sketch f(p)
Solution:
Two points on linear demand function ( 20 , 80000)
(30 , 62500)
Slope = ( 62500 - 80000)/(30 - 20) = -17500/10
= - 1750
20 & 30 are price (p)
80000 & 62500 demand ( quantity) ( q)
q - 80000 = -1750 ( p - 20)
=> q = -1750p + 115000
=> f(p) = q = 115000 - 1750p
determine what price would result in demand of 50000 units
=> 50000 = 115000 - 1750p
=> p = 37.14
Slope is - ve hence increase in demand means decrease in price
domain = ( 0 , 65.71)
range = ( 0 , 115000)
Sketched
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