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# Practice_Problems_answers - Suppose that a firms production...

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Suppose that a firm’s production function is given by : ( ) ( ) (a) What’s the marginal product of labor? Of capital? ( ) ( ) , ( ) ( ) (b) What’s the average product of labor? Of capital? ( ) ( ) ( ) ( ) (c) Does this function satisfy constant, increasing or decreasing returns to scale? Consider the following three cases: For the three cases we have: ( ) (( ) ( ) ) (( )( )) ( ) : ( ) ( ) ( ) so we have constant returns to scale : ( ) ( ) ( ) so we have increasing returns to scale : ( ) ( ) ( ) so we have decreasing returns to scale (d) How many units of capital can we give up if we increase labor by one unit keeping production constant? How do we call this? This is the Marginal rate of Technical Substitution: ( ) ( ) ( ) ( ) ( ) If , the higher is the ratio of capital to labor, the more units of capital can we give up for an additional unit of labor keeping production constant. (e) Compute the elasticity of substitution for this example: First, notice the following: ( ) ( ) ( ) ( ) ( ) Second, since ( ) , ( ) ( ) ( )

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Thus: ( ) ( ) Third, we conclude that ES= *** (f) Repeat the whole exercise for ( ) ( ) , ( ) ( ) ( ) In part (c) consider the following cases: For the three cases we have: ( ) ( ) ( ) (i) : ( ) ( ) so we have constant returns to scale.
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