document.write( "Question 131193This question is from textbook Microeconomics
\n" ); document.write( ": I am taking a class in Economics. The problem I am trying to work is:
\n" ); document.write( "Q=10K^0.5 L^0.5 Q=10K^0.6 L^0.4
\n" ); document.write( "These are production function of two companies where Q is the number of computers produced per day, K is hours of machine time, and L is hours of labor input. We need to find out the output for these equations. The problem asks if both companies use the same amount of capital and labor, which will generate more output?\r
\n" ); document.write( "\n" ); document.write( "How are these problems worked? \n" ); document.write( "

Algebra.Com's Answer #95780 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"Q%5B1%5D+=+%2810%2AK%5E.5%29%2A%28L%5E.5%29\"$
\n" ); document.write( " $\"Q%5B2%5D+=+%2810%2AK%5E.6%29%2A%28L%5E.4%29\"$
\n" ); document.write( "I used subscripts because $\"Q\"$ in the 1st equation
\n" ); document.write( "will not necessarily equal $\"Q\"$ in the 2nd equation
\n" ); document.write( "The problem says $\"K\"$ is the same in both cases
\n" ); document.write( "and $\"L\"$ is the same in both cases
\n" ); document.write( "How does $\"Q%5B1%5D\"$ compare with $\"Q%5B2%5D\"$ ?
\n" ); document.write( "I will set up the ratio $\"j+=+Q%5B1%5D+%2F+Q%5B2%5D\"$
\n" ); document.write( " $\"j+=+%2810%2AK%5E.5%29%2A%28L%5E.5%29+%2F+%2810%2AK%5E.6%29%2A%28L%5E.4%29\"$
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\n" ); document.write( " $\"j+=+%28K%5E%28-.1%29%29%2A%28L%5E.1%29\"$
\n" ); document.write( " $\"j+=+L%5E.1+%2F+K%5E.1\"$ or
\n" ); document.write( " $\"Q%5B1%5D+%2F+Q%5B2%5D+=++L%5E.1+%2F+K%5E.1\"$
\n" ); document.write( "Suppose $\"Q%5B1%5D+=+Q%5B2%5D\"$
\n" ); document.write( " $\"L%5E.1+=+K%5E.1\"$
\n" ); document.write( " $\"L+=+K\"$
\n" ); document.write( "If $\"L+%3E+K\"$ then, $\"Q%5B1%5D+%3E+Q%5B2%5D\"$
\n" ); document.write( "If $\"K+%3E+L\"$ then, $\"Q%5B2%5D+%3E+Q%5B1%5D\"$ \n" ); document.write( "

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