A firm operates in a perfectly competitive market. The firm’s total cost of production is given by the following equation: TC(q) = 100 + 8q2 + 5q, where q is the quantity supplied. What is the shutdown point for this firm in the short run, or in other words, what is the market price below which a firm is better off not supplying any units in the short run? [Advice: draw AVC and MC]
Question
A firm operates in a perfectly competitive market. The firm’s total cost of production is given by the following equation: TC(q) = 100 + 8q2 + 5q, where q is the quantity supplied. What is the shutdown point for this firm in the short run, or in other words, what is the market price below which a firm is better off not supplying any units in the short run? [Advice: draw AVC and MC]
Solution
The shutdown point for a firm in the short run is the price at which the price equals the minimum point of the average variable cost (AVC). Below this price, the firm would not cover its variable costs of production and would be better off shutting down and producing nothing.
First, we need to find the AVC. The total cost (TC) is given by TC(q) = 100 + 8q^2 + 5q. The fixed cost (FC) is 100 (the cost that does not change with the level of output), so the variable cost (VC) is 8q^2 + 5q. The AVC is then VC/q = (8q^2 + 5q) / q = 8q + 5.
Next, we need to find the minimum point of the AVC. To do this, we take the derivative of the AVC with respect to q and set it equal to zero:
d(8q + 5)/dq = 8 = 0
This equation has no solution, which means that the AVC does not have a minimum point. Therefore, the shutdown point for this firm in the short run does not exist. The firm would always cover its variable costs of production, regardless of the market price.
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