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101-12_07 - Econ 101 Lecture 12 A Note on the Firm's...

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Econ 101 Lecture 12 A Note on the Firm’s Shut-Down Condition It might seem that a firm that can sell as much output as it wishes at a constant market price would always do best in the short run by producing and selling the output level for which price equals marginal cost. But there are exceptions to this rule. Suppose, for example, that the market price of the firm’s product falls so low that its revenue from sales is smaller than its variable cost at all possible levels of output. The firm should then cease production for the time being. By shutting down, it will suffer a loss equal to its fixed costs. But by remaining open, it would suffer an even larger loss. If P denotes the market price of the product and Q denotes the number of units produced and sold, then PxQ is the firm’s total revenue from sales, and if we use VC to denote the firm’s variable cost, the rule is that the firm should shut down in the short run if PxQ is less than VC for every level of Q. Average Variable Cost and Average Total Cost Suppose that the firm is unable to cover its variable cost at any level of output—that is, suppose that PxQ < VC for all levels of Q. Then P < VC/Q for all levels of Q, since we obtain the second inequality by simply dividing both sides of the first one by Q. VC/Q = average variable cost —its variable cost divided by its output. The firm’s short-run shut-down condition may thus be restated a second way—namely, discontinue operations in the short run if the product price is less than the minimum value of its average variable cost (AVC). Short-run shut-down condition (alternate version): P < minimum value of AVC Average total cost: ATC = TC/Q. Profit = total revenue (PxQ) – total cost = PxQ – ATCxQ A firm can be profitable only if the price of its product price (P) exceeds its ATC for some level of output. A Graphical Approach to Profit-Maximization For Louisville Slugger, we have Employees per day Bats per day Variable cost ($/day) Average variable cost ($ per unit of output) Total cost ($/day) Average total cost ($ per unit of output) Marginal cost ($/bat) 0 0 0 80 0.60 1 40 24 0.60 104 2.60 0.40 2 100 48 0.48 128 1.28 0.80 3 130 72 0.554 152 1.169 1.20 4 150 96 0.64 176 1.173 1.60 5 165 120 0.727 200 1.21 2.40 6 175 144 0.823 224 1.28 4.00 7 181 168 0.928 248 1.37
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2 Properties of the cost curves: 1. The upward sloping portion of the marginal cost curve (MC) corresponds to the region of diminishing returns. Thus, as the
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