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Unformatted text preview: Chapter 22 NAME Firm Supply Introduction. The shortrun supply curve of a competitive firm is the portion of its shortrun marginal cost curve that is upward sloping and lies above its average variable cost curve. The longrun supply curve of a competitive firm is the portion of its shortrun marginal cost curve that is upwardsloping and lies above its longrun average cost curve. Example: A firm has the longrun cost function c ( y ) = 2 y 2 + 200 for y > 0 and c (0) = 0. Let us find its longrun 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 longrun marginal cost curve is an upwardsloping straight line through the origin with slope 4. The longrun supply curve is the portion of this curve that lies above the longrun average cost curve. When output is y , longrun 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 longrun supply curve is the piece of the longrun marginal cost curve for which y > 10. So the longrun 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 longrun 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. 272 FIRM SUPPLY (Ch. 22) 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....
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This note was uploaded on 05/05/2010 for the course ECONMOICS ECON 203 taught by Professor Josephpetry during the Spring '10 term at University of Illinois, Urbana Champaign.
 Spring '10
 JOSEPHPETRY

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