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solutions_Chapter22

# solutions_Chapter22 - Chapter 22 NAME Firm Supply...

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Chapter 22 NAME Firm Supply Introduction. The short-run supply curve of a competitive Frm 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 Frm 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 Frm has the long-run cost function c ( y )=2 y 2 + 200 for y> 0and c (0) = 0. Let us Fnd its long-run supply curve. The Frm’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 Fnd 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 Frm are AC ( y y + 200 /y .Th i si sa 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 Fnd that AC ( y ) ( y )when 10. Therefore the long-run supply curve is the piece of the long-run marginal cost curve for which 10. So the long-run supply curve has the equation p =4 y for 10. If we want to Fnd quantity supplied as a function of price, we just solve this expression for y as a function of p .Thenw ehav e y = p/ 4 whenever p> 40. Suppose that p< 40. ±or example, what if p = 20, how much will the Frm supply? At a price of 20, if the Frm produces where price equals long-run marginal cost, it will produce 5 = 20 / 4 units of output. When the Frm produces only 5 units, its average costs are 2 × 5 + 200 / 5 = 50. Therefore when the price is 20, the best the Frm 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 o² producing nothing at all. In fact, for any price 40, the Frm 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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278 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 proFts. On the above graph, shade in and label the following areas: total costs, total revenue, and total proFts.
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solutions_Chapter22 - Chapter 22 NAME Firm Supply...

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