Two local ready-mix cement manufacturers,Here and There,have combined demand given by Q = 105 - P.Their total costs are given by TC_Here = 5Q_Here + 0.5Q²_Here and TC_There = 5Q_There + 0.5Q²_There.If they successfully collude,their total output will be:

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In a collusive duopoly, the two firms act as if they were a monopolist and share the profits equally. Therefore, they will produce the output level that maximizes their joint profits. The marginal cost of each firm is 5, so the combined marginal cost is 10. To maximize profits, they will produce the level of output where marginal revenue equals marginal cost. The total demand function is Q = 105 - P. Solving for price, we get P = 105 - Q. Then, total revenue is TR = P × Q = (105 - Q) × Q = 105Q - Q^2. Marginal revenue is the derivative of total revenue with respect to quantity. So, MR = dTR/dQ = 105 - 2Q. Setting MR = MC, we get 105 - 2Q = 10. Solving for Q, we get Q = 47.5. Since each firm produces half of the output, each will produce Q/2 = 47.5/2 = 23.75. Rounded to the nearest unit, this gives a combined output of 24 × 2 = 48 units. However, we need to check whether this output level makes both firms better off than if they each produced competitively. If it does not, then the firms will have an incentive to cheat on the agreement and produce more than the agreed-upon quantity. Under competition, the output of each firm is determined by marginal cost, so they will produce where MC = P. From the demand function, P = 105 - Q, so MC = 105 - Q. Setting MC = P, we get 105 - Q = Q, or Q = 52.5. Each firm produces 52.5/2 = 26.25 units, and the total output is 2 × 26.25 = 52.5 units. The total cost for each firm at an output of 26.25 is: TC_Here = 5 × 26.25 + 0.5 × (26.25)^2 = $347.34 TC_There = 5 × 26.25 + 0.5 × (26.25)^2 = $347.34 The total cost for both firms together is $694.68. Under collusion, the total cost is: TC_Here = 5 × 23.75 + 0.5 × (23.75)^2 = $326.41 TC_There = 5 × 23.75 + 0.5 × (23.75)^2 = $326.41 The total cost for both firms together is $652.82. This means that the collusive output level of 48 units is indeed better for the firms than the competitive output level of 52.5 units. Therefore, the firms will stick to the collusive agreement and produce a total output of 2 × 23.75 = 47.5 units, rounded to 40 units.

Two Local Ready-Mix Cement Manufacturers,Here and There,have Combined Demand Given