lec18 - 2010-04-07 Production Allocation Decision $/unit of...

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2010-04-07 1 Profit Maximization II MC 2 15 20 MC 1 Production Allocation Decision $/unit of output What is lowest cost allocation of production to produce 20 units of output in two factories? TC 1 =5q 1 + (q 1 ) 2 /2 TC 2 =(q 2 ) 2 /2 MC 1 = 5 + q 1 MC 2 = q 2 10 20 5 10 q How much should each factory produce? MC 2 15 20 MC 1 Production Allocation Decision $/unit of output What is lowest cost allocation of production to produce 20 units of output in two factories? TC 1 =5q 1 + (q 1 ) 2 /2 TC 2 =(q 2 ) 2 /2 MC 1 = 5 + q 1 MC 2 = q 2 12 5 10 20 5 10 q How much should each factory produce? 7.5 12.5 12.5 MC 2 15 20 MC 1 Numerical Solution: Production Allocation Decision $/unit of output MC 1 = 5 + q 1 MC 2 = q 2 and q 1 + q 2 = 20 12 5 Solve for q 1 and q 2 : 5 + q 1 = q 2 (MC 1 = MC 2 ) q 2 = 20 – q 1 (q 1 + q 2 = 20) 10 20 5 10 q 7.5 12.5 12.5 5 + q 1 = 20–q 1 2q 1 = 15 q 1 = 7.5 Î q 2 = 12.5 Any other allocation will be more costly. Why? Profit-Maximizing Input Levels We know we should produce where MR = MC What does that tell us about the level of inputs to use?
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This note was uploaded on 09/18/2010 for the course ECON 201 taught by Professor Beomsookim during the Fall '10 term at Korea University.

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lec18 - 2010-04-07 Production Allocation Decision $/unit of...

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