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Macroeconomics Exam Review 250

# Macroeconomics Exam Review 250 - Solutions for Foundations...

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Rearranging and using the bilinearity of 𝑓 gives 𝑓 ( x 1 x 2 , 𝜽 1 ) 𝑓 ( x 1 x 2 , 𝜽 2 ) and 𝑓 ( x 1 x 2 , 𝜽 1 𝜽 2 ) 0 6.4 Let 𝑝 1 denote the profit maximizing price with the cost function 𝑐 1 ( 𝑦 ) and let 𝑦 1 be the corresponding output. Similarly let 𝑝 2 and 𝑦 2 be the profit maximizing price and output when the costs are given by 𝑐 2 ( 𝑦 ). With cost function 𝑐 1 , the firms profit is Π = 𝑝𝑦 𝑐 1 ( 𝑦 ) Since this is maximised at 𝑝 1 and 𝑦 1 (although the monopolist could have sold 𝑦 2 at price 𝑝 2 ) 𝑝 1 𝑦 1 𝑐 1 ( 𝑦 1 ) 𝑝 2 𝑦 2 𝑐 1 ( 𝑦 2 ) Rearranging 𝑝 1 𝑦 1 𝑝 2 𝑦 2 𝑐 1 ( 𝑦 1 ) 𝑐 1 ( 𝑦 2 ) (6.31) The increase in revenue in moving from 𝑦 2 to 𝑦 1 is greater than the increase in cost. Similarly 𝑝 2 𝑦 2 𝑐 2 ( 𝑦 2 ) 𝑝 1 𝑦 1 𝑐 2 ( 𝑦 1 ) which can be rearranged to yield 𝑐 2 ( 𝑦 1 ) 𝑐 2 ( 𝑦 2 ) 𝑝 1 𝑦 1 𝑝 2 𝑦 2 Combining the previous inequality with (6.31) yields 𝑐 2 ( 𝑦 1 ) 𝑐 2 ( 𝑦 2 ) 𝑐 1 ( 𝑦 1 )
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