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 25 degrees Celsius or higher—demand for vending machine soft drinks is: Q = 300 − 2P .

On “cool” days—when the outside temperature is below 25 degrees Celsius—demand is: Q =200 − 2P . The marginal cost of a canned 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?

b. Suppose that half of the days are “hot” and the other half are “cool.” If CocaCola uses a traditional machine that is programmed to charge the same price regardless of the weather, what price should it set?

c. Compare Coca-Cola’s profit from a weather-sensitive machine to the traditional, uniform pricing machine.

Answer 1

Answer (a): It is given that on ‘Hot’ days the demand for Coca-Cola is Q = 300 – 2P

                                                                                                                        >    Q + 2P = 300

                                                                                                                        >     2P = 300 – Q

                                                                                                                        > P = (300 – Q)/2

                                                                                                                        > P = 150 – 1/2Q

                                                          Therefore, Marginal Revenue     = 150 – Q

                                                                                     Which must be : 150 – Q = 20

                                                                                                                 Q = (150-20)

                                                                                         & Price = 150 – ½ X 130

                                                                                                       = 150 – 75

                                                                                                       = 85   

& It is given that on ‘Cold’ days the demand for Coca-Cola is Q = 200 – 2P

                                                                                                                        >    Q + 2P = 200

                                                                                                                        >     2P = 200 – Q

                                                                                                                        > P = (200 – Q)/2

                                                                                                                        > P = 100 – 1/2Q

                                                          Therefore, Marginal Revenue     = 100 – Q

                                                                                     Which must be : 100 – Q = 20

                                                                                                                 Q = (100-20)

                                                                                         & Price = 100 – ½ X 80

                                                                                                       = 100 – 40

                                                                                                       = 60

Therefore, on Hot days, the price of Coca-Cola should be 85 cents and on Cold days the price of Coca-Cola should be 60 cents.                              

                        

Answer (b): As It is given that half the number of days are Cold and half of the number of days are Hot, in this case the average aggregate demand encountered by the company will be:

                                                Q = ½ (300 – 2P) + ½ (200 – 2P)

• Q = (150 +100) – (P+P)
• Q = 250 – 2P

Therefore, the Marginal revenue encountered by the company will be = 125 -Q

                                                   Which will be: 125 – Q = 20

                                                                               Q = 125 – 20

                                                                                   = 105

And the Price will be: 150 = 250 – 2P

                                       Therefore, Price = 150/2

                                                                    = 72.5

Answer (c): As per the given conditions, the profits for the company will be = ½ (85 – 20) 130 + (60 – 20)80

= 0.5 (85-20)130 + 40x80

= 5825

& When the discrimination of the price is non-existent, the profit for firm will be= (150/2 – 20) x 105

                                                                                                                                                = 5512.5

Therefore, we can see that the profit for the firm will be higher when the discrimination exists.