Suppose that Coca-Cola uses a new type of vending machine that charges a price a
ID: 1112185 • Letter: S
Question
Suppose that Coca-Cola uses a new type of vending machine that charges a price according to the outside temperature. On “hot” days – defined as days in which the outside temperature is 77 degree Fahrenheit or higher – demand for vending machine soft drinks is Q = 300 – 2P. On “cool” days – when the outside temperature is below 77 degree Fahrenheit – demand is Q = 200 – 2P. The marginal cost of a soft drink is 20 cents.
(a) What price should the machine charge for a soft drink on “hot” days? What price should it charge on “cool” days? Please show your work.
(b) Suppose that half of the days are “hot” and the other half are “cool.” If Coca-Cola uses a traditional machine that is simply programmed to charge the same price regardless of the weather, what price should it set? Please show your work.
(c) Compare Coca-Cola’s profit from a weather-sensitive machine to the traditional, uniform pricing machine.
Explanation / Answer
a) on hot days = Q = 300 - 2P
or P = 150 - 0.5Q
MR = 150 - Q and MC = 20
now MR=MC
150-Q = 20 or Q = 130
P = 150 - 65 = $85
on cool days, Q =200-2P
P = 100 - 0.5Q
MR = 100 - Q and MC = 20
100 -Q = 20
Q = 80
P = 100 - 40 = $60
so, on hot days, the price they charge is $85 and on cool days they price charge= $60
b) total demand , Q = 500-4P
P = 125 - 0.25Q
MR = 125 - 0.5Q and MC = 20
125-0.5Q = 20
0.5Q = 105 or Q = 210
and P = 125 - 0.25*210 = $72.5
so, they charge price equal to $72.5
c) we cannot measure profit with total cost. but according to the total revenue, profit is maximizng when when producing form weather-sensitive machine . because total reveue is large when it produce when weather sensitive machine than a total revenue in traditional machine.