Suppose that the demand for the Amazon Fire Tablet is given

Suppose that the demand for the Amazon Fire Tablet is given by QDk = 800150Pk +50Pi, where QDk is the quantity demanded for Amazon Fire Tablet, Pk is the price of a Amazon Fire Tablet and Pi is the price of an iPad Minis. Also assume that the demand for the iPads Minis is given by QDi = 900 100Pi + 20Pk. Finally, assume that the supply for Amazon Fire Tablet and the iPad Minis are simply given by QSk = 700 + 350Pk and QSi = 800 + 300Pi. Find the equilibrium price of iPad Minis.

Solution

At equilibrium, the supply and demand values will be equal for both Amazon Fire Tablets as well as the IPad Minis.

So, for Amazon Fire Tablet, QD_k = QS_k yields-

800 - 150 (P_k) + 50 (P_i) = 700 + 350 (P_k)

=> 800 - 700 = 350 (P_k) + 150 (P_k) - 50 (P_i)

=> 100 = 500 (P_k) - 50 (P_i)

Dividing each side by 50 we get -

=> 2 = 10 (P_k) - (Pi)

or, 10 (P_k) - (P_i) = 2-------------------------------------------------------- (i)

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And, for the iPad Minis, the equation QD_i = QS_i yields -

900 - 100 (Pi) + 20 (P_k) = 800 + 300 (Pi)

=> 900 - 800 = 300 (Pi) + 100 (Pi) - 20 (P_k)

=> 100 = 400 (Pi) - 20 (P_k)

Dividing each side by 20 we get -

=> 5 = 20 (Pi) - (P_k)

or, 20 (Pi) - (P_k) = 5-----------------------------------------------------------------------(ii)

Now, multiplying the equation (ii) by 10 and adding it to (i) we get -

200 (P_i) - 10 (P_k) + 10 (P_k) - (P_i) = 50 + 2

=> 199 (Pi) = 52

=> (P_i) = 52/199 = 0.2613065

Hence, the equilibrium price of iPad Minis = 0.2613065.