Product Differentiation:

1) Model:

* Small Car Market (Oligopoly)

Two Firms: Ford (Firm 1) and Toyota (Firm 2) with Focus and Echo, respectively.

* For simplicity, assume that MC_F = AC_F = c = AC_T = MC_T.

Demand facing Ford is assumed to be Q_F = a − P_F +β . P_T ............(i).

* If β > 0, the increase in P_T will increase Q_F. It means Focus as well as Echo are substitutes.

* If β < 0, two products are complements.

2) Analysis:

Let’s get best response of Ford to P_T.

π_F = (PF − c)Q_F = (P_F − c)(a − P_F + β . P_T) ..........(ii)

dπ_F/dP_F = + − 2 P_F + β.P_T = 0 ........(iii)

The reasonable price PF is PF = (a + c + β.P_T)/ 2  (iv) (Ford’s reaction curve to Toyota’s price) For example, if Toyota sells Echo at P_T = c , then Ford’s best way to maximize its profit is to sell Focus at P_F = (a + c + βc)/ 2

Suppose the demand facing Toyota is Q_T = a − P_T + β . P_F  ..........(v)

In the same way, we can get P_T = (a + c + β.P_F)/2 ...........(vi)

Point a and c: (a +c)/2
Point b and d: (a +c)/2-β

If 0 < β < 2, then Focus and Echo have substitutability in some degree.

If β < 0 , we get the same results. But reaction curves are downward sloping.
If β > 2 , PF *, PT * < 0 . In practice, PF * = PT * = c

As β goes up, the substitutability will go up, which means there are almost identical products.

Therefore it is same in the perfect competition pricing.

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