Macroeconomics Exam Review 60

Macroeconomics Exam Review 60 - For analysis, it is...

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Unformatted text preview: For analysis, it is convenient to represent the technology ( ) by a production function (Example 2.24). The firms optimization can then be expressed as max x + ( x ) =1 and the profit function as ( , w ) = max x + ( x ) =1 2.14 1. Assume that production is profitable at p . That is, there exists some y such that ( y , p ) > 0. Since the technology exhibits constant returns to scale, is a cone (Example 1.101). Therefore y for every > 0 and ( y , p ) = ( ) = = ( y , p ) Therefore { ( y , p ) : > } is unbounded and ( p ) = sup y ( y , p ) sup > ( y , p ) = + 2. Assume to the contrary that there exists p + with ( p ) = / { , + , } ....
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