Final answer:
In a homogeneous-product market with two identical firms, each having a capacity of 3 units and a marginal cost of 0, setting the price at $3 can sustain an equilibrium. Each firm would sell at full capacity, earning a profit of $9, since their total revenue would be $9 and costs are zero.
Step-by-step explanation:
The student's question concerns the possibility of sustaining an equilibrium where both firms set the same price in a perfectly competitive, homogeneous-product market, when each firm has a finite capacity and faces constant marginal costs of zero up to that capacity constraint. Given the market demand function Q(p) = 9 - p, we need to determine if p1 = p2 = 3 can be held as an equilibrium and to calculate the equilibrium profits.
Profits (π) of a firm in such a market are determined by the equation π = (Price)(Quantity produced) - (Average cost)(Quantity produced). In a perfectly competitive market, firms are price-takers and sell their product at the market price, which in this case, is proposed to be $3 for each firm. Given that marginal costs are zero up to their capacity of 3 units, setting the price at $3 would mean that each firm produces and sells at full capacity, as the price equals the marginal cost at that point, which leads to the efficient allocation of resources.
At a price of $3, the demand according to the demand function would be Q(3) = 9 - 3 = 6. Since the two identical firms split the market evenly when pricing equally, each firm would supply 3 units, completely utilizing their capacity. The total revenue for each firm would be 3 units * $3 = $9, while the cost is zero (since the marginal cost up to their capacity is zero). Therefore, each firm's profit would be $9. As marginal cost equals marginal revenue and total revenue exceeds total costs by the greatest amount, this price can be considered an equilibrium.