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Assume the tobacco industry is made up of 30 firms with the cost function c(q)= 1/2(q² +2 and 40 firms with cost function c(q)=q². Assume no new firms can enter the industry due to regulations. What would be the long-run industry supply curve (i.e. aggregate supply)? (Hint: be careful, market participation depends on market prices).

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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.

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