Question

The Coca Cola vending machines

Suppose that Coca-Cola uses a new type of vending machines that charge a price p (in cents)
according to the outside temperature. On “hot” days when the temperature is above 20◦
Celsius, demand for soft drinks is D(p) = 300 − 2p. On “cool” days when the temperature
is below 20◦ Celsius, demand for soft drinks is D(p) = 200 − 2p. The unit cost of a drink is
20 cents.
1. What price should the machine charge on “hot” and on “cool” days?
2. Suppose 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?
3. Compare Coca-Cola’s profit from a weather-sensitive machine and from a traditional
machine?
4. Suppose Coca-Cola rents these machines. If the cost per day of a weather-sensitive
machine exceeds by 10 euros the cost of a traditional machine, what sort of machines
should Coca-Cola rent?

Answer 1

1) On hot days MR=MC ,

so p= (300-q)/2 ,

TR=P*Q= 150q-q²/2

MR= 150-q

MC=MR is the profit maximising condition which is given by

20= 150-q

q=130 , putting q=130 , we get

p=(300-130)/2= 170/2=85 cents

On cold days

p= (200-q)/2 ,

TR=P*Q= 100q-q²/2

MR= 100-q

MC=MR is the profit maximising condition which is given by

20= 100-q

q=80 , putting q=80 , we get

p=(200-80)/2= 120/2=60 cents

2) If half of the days are cold and the other half are hot , we need to find the new price.

For that the demand of each should be halved ie

Q=Qh+Qc= 300-2P+200-2P= 250-2p

TR=(250Q-Q²)/2 , so MR= 125-Q

MR=MC

125-Q=20

105= Q , putting it in the demand equation we get

P= (250-105)/2= 145/2= 72.5 cents

3) Profit is given by

Profit in case of different prices =TR-TC

= [(85*130-130*20)]+(80*60-80*20]/2

(The costs and revenue of each type is calculated separately and the whole sum is halved because the probability of each happening is 0.5)

= 8450+3200/2=5825 cents= $58.25

Profit in case of same price = TR-TC

= 72.5*105-20*105

= 5512.5= $55.12

Profits are higher in case of separate price for hot and cold .

4) If the rent of machines per day exceeds for weather sensitive machine , it should not be rented because the difference in profit in these two machines is less than 10 euro and the firm would find it less profitable due to the additional cost of machine.

In such a case the traditional machine should be rented.

(You can comment for doubts )