supplyspring07 - 12 98 y 2 = 0 . Solution is: y = 7 At AC...

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Supply - Example 1 Supply example 1.1 Long run supply Consider a long run cost function c ( y )=2 y 3 12 y 2 +72 y. AC: 2 y 2 12 y +72 MC: 6 y 2 24 y +72 The minimum of AC: AC 0 =4 y 12 = 0 . The minimum is at y =3 with AC (3) = 54 . For prices above p =54 supply is such that p = MC . Hence the inverse supply for y> 3 is. p =6 y 2 24 y +72 . Solving for y as a function of p, (and choosing the larger quantity of the two solutions) we f nd supply: y = ½ 0 p< 54 1 6 6 p 48 + 2 p> 54 10 7.5 5 2.5 0 100 75 50 25 0 y p (Graph incomplete) 1
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1.2 Short run supply Suppose there is a short run cost given by: c ( y )= y 3 12 y 2 +60 y +98 . AC y 2 12 y +60+ 98 y MC: 3 y 2 24 y +60 VC ( y )= y 3 12 y 2 +60 y AVC: y 2 12 y +60 The minimum of AVC: AV C 0 =2 y 12 = 0 . The minimum is at y =6 with cost AV C (6) = 24 . The minimum of the AC AC’= 2 y
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Unformatted text preview: 12 98 y 2 = 0 . Solution is: y = 7 At AC (7) = 39 For prices above the p = 24 supply is such that p = MC . Hence the inverse supply for y &gt; 6 is p = 3 y 2 24 y + 60 . Supply is y = p &lt; 24 1 3 3 p 12 + 4 p &gt; 24 10 7.5 5 2.5 80 60 40 20 y p (Graph incomplete). For prices which are below 24, the f rm is losing its f xed cost, pro f t is F = 98 .. For prices between 24 and 39, the f rm is loosing money, but not as much as it would with zero production. Only with prices above 39 its the f rms short run pro f t positive. 2...
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supplyspring07 - 12 98 y 2 = 0 . Solution is: y = 7 At AC...

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