Assume that all firms in a competitive industry have cost curves given by the following: TC = 15 +8q +9q2. In the short-run, the price at which a firm will start to shut down is
Question
Assume that all firms in a competitive industry have cost curves given by the following: TC = 15 +8q +9q2. In the short-run, the price at which a firm will start to shut down is
Solution
The shutdown point for a firm in the short run is the point where the price is equal to the minimum average variable cost (AVC). If the price falls below this point, the firm would be better off shutting down and not producing anything, as it would be losing money on each unit of output.
The total cost (TC) function given is TC = 15 + 8q + 9q^2. This includes both fixed costs (FC) and variable costs (VC). In this case, the fixed cost is 15 (the part of the total cost that does not change with the quantity of output).
The variable cost (VC) is the part of the total cost that changes with the quantity of output. In this case, it is 8q + 9q^2.
The average variable cost (AVC) is the variable cost divided by the quantity of output, or AVC = VC/q. Substituting the given variable cost, we get AVC = (8q + 9q^2) / q = 8 + 9q.
The minimum AVC is the lowest point on the AVC curve. To find this, we take the derivative of the AVC with respect to q, set it equal to zero, and solve for q.
The derivative of 8 + 9q with respect to q is 9. Setting this equal to zero, we get 9 = 0, which has no solution. This means that the AVC is always increasing and does not have a minimum point.
Therefore, the price at which a firm will start to shut down is the price equal to the AVC when q = 0, which is 8. If the price falls below 8, the firm would be better off shutting down in the short run.
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