#### Product Differentiation, model and analysis

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 MCF = ACF = c = ACT = MCT.

Demand facing Ford is assumed to be QF = a − PF +β . PT ............(i).

* If β > 0, the increase in PT will increase QF. 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 PT.

πF = (PF − c)QF = (PF − c)(a − PF + β . PT) ..........(ii)

F/dPF = + − 2 PF + β.PT = 0 ........(iii)

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

Suppose the demand facing Toyota is QT = a − PT + β . PF  ..........(v)

In the same way, we can get PT = (a + c + β.PF)/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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