pls answer 1&2 question thanks a lot

Consider a duopoly market, where two firms sell differentiated prod- ucts, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices p1 and p2 simultaneously. The derived demand functions for the two firms are: D1 (p1, p2) = 5 + 12, P1 and D2 (P1, P2) = 2 PI-P2, where S' > 0 and the parameter t > 0 measures the degree of product differentiation. Both firms have constant marginal cost c > 0 for production. From the demand functions, qi = Di (Pi, pi) = 2 + Pi Pi ", deriv the residual inverse demand functions: p; = Pi(qi, P;) (work ou Pi(qi, p;)). Show that for t > 0, Pi(qi, p;) is downward-sloping i . e . , aqi OP: (96.P) c, i.e., firm i has market power. Calculate the limits of the equilibrium prices and profits as t - 0. What is Pi(qi, p;) as t - 0? Is it downward sloping? Ar gue that the Bertrand Paradox (i.e., the prediction of the stati Bertrand duopoly model, where pi = p> = c) holds only in th extreme case of t