# 22 - Chapter 22 NAME Firm Supply Introduction The short-run...

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Chapter 22 NAME Firm Supply Introduction. The short-run supply curve of a competitive firm is the portion of its short-run marginal cost curve that is upward sloping and lies above its average variable cost curve. The long-run supply curve of a competitive firm is the portion of its short-run marginal cost curve that is upward-sloping and lies above its long-run average cost curve. Example: A firm has the long-run cost function c ( y ) = 2 y 2 + 200 for y > 0 and c (0) = 0. Let us find its long-run supply curve. The firm’s marginal cost when its output is y is MC ( y ) = 4 y . If we graph output on the horizontal axis and dollars on the vertical axis, then we find that the long-run marginal cost curve is an upward-sloping straight line through the origin with slope 4. The long-run supply curve is the portion of this curve that lies above the long-run average cost curve. When output is y , long-run average costs of this firm are AC ( y ) = 2 y + 200 /y . This is a U- shaped curve. As y gets close to zero, AC ( y ) becomes very large because 200 /y becomes very large. When y is very large, AC ( y ) becomes very large because 2 y is very large. When is it true that AC ( y ) < MC ( y )? This happens when 2 y +200 /y < 4 y . Simplify this inequality to find that AC ( y ) < MC ( y ) when y > 10. Therefore the long-run supply curve is the piece of the long-run marginal cost curve for which y > 10. So the long-run supply curve has the equation p = 4 y for y > 10. If we want to find quantity supplied as a function of price, we just solve this expression for y as a function of p . Then we have y = p/ 4 whenever p > 40. Suppose that p < 40. For example, what if p = 20, how much will the firm supply? At a price of 20, if the firm produces where price equals long-run marginal cost, it will produce 5 = 20 / 4 units of output. When the firm produces only 5 units, its average costs are 2 × 5 + 200 / 5 = 50. Therefore when the price is 20, the best the firm can do if it produces a positive amount is to produce 5 units. But then it will have total costs of 5 × 50 = 250 and total revenue of 5 × 20 = 100. It will be losing money. It would be better off producing nothing at all. In fact, for any price p < 40, the firm will choose to produce zero output. 22.1 (0) Remember Otto’s brother Dent Carr, who is in the auto repair business? Dent found that the total cost of repairing s cars is c ( s ) = 2 s 2 + 100. (a) This implies that Dent’s average cost is equal to 2 s + 100 /s , his average variable cost is equal to 2 s , and his marginal cost is equal to 4 s . On the graph below, plot the above curves, and also plot Dent’s supply curve.

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272 FIRM SUPPLY (Ch. 22) 0 5 10 15 20 20 40 60 Output Dollars 80 Supply mc ac avc Revenue Costs Profit (b) If the market price is \$20, how many cars will Dent be willing to repair? 5. If the market price is \$40, how many cars will Dent repair? 10. (c) Suppose the market price is \$40 and Dent maximizes his profits. On the above graph, shade in and label the following areas: total costs, total revenue, and total profits.
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