תחרות מחירים עם סחורות ממוינות בשוק ברטראן

In the Bertrand model with differentiated products, companies compete by setting prices for goods that are similar but not identical. Differentiation reduces direct substitutability between products, giving firms more control over pricing.

Consider the automotive market as an example. Tesla and Ford compete in the electric vehicle segment, offering distinct and differentiated products. 

Tesla’s demand depends on its price P_T and Ford’s price P_F, while Ford’s demand also depends on both its price P_F and Tesla’s price P_T​.

The quantities sold by Tesla and Ford, denoted as Q_Tand Q_F, respectively, depend on their demand functions.

These functions capture the influence of cross-price sensitivity and how changes in one firm’s price affect the other’s demand. 

To simplify the analysis, it is assumed that both firms set their prices simultaneously, face fixed costs, and operate with similar demand structures.

Thus, Tesla’s demand function is Q_T = D_T - 2P_T + P_F, where D_T​ represents Tesla’s baseline demand.

Similarly, Ford's demand behaves as Q_F = D_F - 2P_F + P_T, where D_F is Ford’s baseline demand.

This framework highlights the strategic pricing interdependence in markets with differentiated product