(i) Firm i's profit maximization problem can be stated as: ni = (a - P: + bpj - c)q: where ni is the profit of firm i, p: is the price charged by firm i, and q: is the quantity produced by firm i. Substituting the demand function for q:, we get: ni = (a - P: + bpj - c)(a - p: + bpj) To maximize profit, we take the first derivative of the profit function with respect to p: and set it equal to zero: anti/ap: = -2(a - P: + bpj - c) + b(a - pj + bp;) = 0 Simplifying, we get: P: = (a + bpj - c)/(2 - b) This is firm i's best-response function, which shows the optimal price that firm i should charge given the price charged by firm j. (ii) Similarly, firm j's profit maximization problem can be stated as: nj = (a - pj + bpi - c)qi where nj is the profit of firm j, pj is the price charged by firm j, and qi is the quantity produced by firm j. Substituting the demand function for qj, we get: nj = (a - pj + bpi - c)(a - pj + bpj) To maximize profit, we take the first derivative of the profit function with respect to pj and set it equal to zero: anj/apj = -2(a - pj + bpi - c) + b(a - p: + bpj) = 0 Simplifying, we get: pj = (a + bpi - c)/(2 - b) This is firm j's best-response function, which shows the optimal price that firm j should charge given the price charged by firm