Final answer:
To determine the long-run industry supply curve in the tobacco industry, we need to consider the cost functions of the firms. By finding the quantity supplied by each firm at different prices and summing them up, we can obtain the industry supply curve.
Step-by-step explanation:
In order to determine the long-run industry supply curve, we need to consider the cost functions of the firms in the tobacco industry. The cost function for 30 firms is c(q) = ½ q² + 2 and for 40 firms is c(q) = q². Since no new firms can enter the industry, the long-run industry supply curve will be the horizontal summation of the individual firms' supply curves.
To find the industry supply curve, we need to find the quantity supplied by each firm at various prices and then sum up the quantities. The quantity supplied by each firm can be obtained by setting the cost function equal to the market price and solving for quantity. Once we have the quantities supplied by each firm, we can sum them up to get the industry supply curve.
Let's consider the cost function c(q) = ½ q² + 2 for the 30 firms. If the market price is P, then c(q) = ½ q² + 2 = P. Solving for q, we get q² = 2(P - 2) and q = sqrt(2(P - 2)). By plugging in different values of P, we can find the corresponding quantities supplied by each firm. Similarly, we can do the same for the cost function c(q) = q² for the 40 firms.