Final answer:
The long-run industry supply curve in the tobacco industry, consisting of 30 firms with cost function c(q) = 1/2(q^2 + 2) and 40 firms with cost function c(q) = q^2, is a horizontal line at q = 0, representing the aggregate quantity supplied by all firms in the industry.
Step-by-step explanation:
In a long-run equilibrium, the industry supply curve represents the aggregate quantity supplied by all firms in the industry at each price level. To determine the long-run industry supply curve, we need to consider the cost functions of the firms involved. In this case, we have two cost functions: c(q) = 1/2(q^2 + 2) for 30 firms and c(q) = q^2 for 40 firms in the tobacco industry.
First, let's find the quantity at which each firm has minimum average cost. For c(q) = 1/2(q^2 + 2), we take the derivative of the cost function with respect to q and set it equal to zero:
c'(q) = q = 0
This implies that the minimum average cost occurs at q = 0. For c(q) = q^2, we differentiate the cost function:
c'(q) = 2q = 0
Again, q = 0 is the quantity at which the minimum average cost is achieved.
Since there are no new firms entering the industry, the long-run industry supply curve is determined by the existing firms. The long-run industry supply curve is simply the sum of the individual firms' supply curves, which are horizontal lines at their respective quantities with minimum average cost. Therefore, the long-run industry supply curve is a horizontal line at q = 0, representing the aggregate quantity supplied by all firms in the industry.