Math 165 Linear Price - Demand Model
Math 165 Linear Price - Demand Model
See Example 1.4.5 on p. 47 .
The phrase
for each $1 increase in the price, 400 fewer cassettes are sold
can be expressed mathematically as
change in demand
change in price
 = -400
1.00
 ,
a constant (for each ).
Another statement:
the rate of change of demand with respect to price is [(-400)/1.00], a constant
Using the point-slope form for the demand, q, in terms of the price, p,
q = q0 + fixed ratio
(-400/1.00)

 
 (p - p0),
with q0 = 4000, and p0 = 5.00, so that

q = 4000 + -400
1.00
 (p - 5.00).
We could also restate
for each $1 increase in the price, 400 fewer cassettes are sold
as
change in price
change in demand
 = 1.00
-400
 ,
a constant.
Another statement:
the rate of change of price with respect to demand is [1.00/(-400)],
or
Using the point-slope form for the price, p, in terms of the demand, q,
p = p0 + 1.00
-400
 (q - q0),
with q0 = 4000, and p0 = 5.00, so that
p = 5.00 + 1.00
-400
 (q - 4000).
Examples
1.
for each 0.50 increase in the price, 120 fewer cassettes are sold
q
= q0 + -120
0.50
 (p - p0),
p
= p0 + 0.50
-120
 (q - q0).
We could interpret [(p - p0)/0.50] as the number of 0.50 price increases.
2.
for each 0.25 increase in the price, 140 fewer cassettes are sold
q
= q0 + -140
0.25
 (p - p0),
p
= p0 + 0.25
-140
 (q - q0).
3.
for each 0.08 increase in the price, 56 fewer cassettes are sold
q
= q0 + -56
0.08
 (p - p0),
p
= p0 + 0.08
-56
 (q - q0).
4.
for each 0.10 increase in the fare, there are 180 fewer riders
q
= q0 + -180
0.10
 (p -p0),
p
= p0 + 0.10
-180
 (q - q0).
5.
for each 0.08 increase in the fare, there are 300 fewer riders
q
= q0 + -300
0.08
 (p - p0),
p
= p0 + 0.08
-300
 (q - q0).


File translated from TEX by TTH, version 3.79.
On 13 Feb 2008, 08:37.