Consider two firms named F1 and F2, producing quantities q1 and q2 of a commodity respectively, with constant marginal costs c1 = c2 = 4 s respectively, where s=9. The two firms face the inverse demand function p = 200 Q, where Q = q1 + q2 and are in Stackelberg competition with firm F1 moving first.

(i) Compute the equilibrium quantities q1* and q2* produced and the corresponding equilibrium price p* in this market.

(ii) Suppose that this market takes place repeatedly in days t = 0, 1, 2, . . .. At t = 0 firm F1 sets an output q1,0 > q1* and each day thereafter it adjusts output according to the process:

q1,t = q1,t1+(q1*q1,t1), where (1, 2). Study the resulting dynamic process and compute the time path of the equilibrium price.

(iii) Explain carefully whether or not some day(s) is (are) more favorable to purchase this commodity.

(iv) Suppose you have decided to buy this commodity after t = s when you receive your salary, where s=9. Explain whether or not there is some day most favorable to make your purchase.