prodprobs

prodprobs - elasticity of substitution in this case B...

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CES Problems, November 2007 1) There are two factors and the production function is F ( x 1 , x 2 ) = Min { x 1 a 1 , x 2 a 2 } A) Draw the unit isoquant in the x 1 , x 2 plane. B) Calculate x ( w 1 , w 2 , 1) and c ( w 1 , w 2 , 1) where x ( w 1 , w 2 , 1) = ( x 1 ( w 1 , w 2 , 1) , x 2 ( w 1 , w 2 , 1)) is the conditional factor demand for producing one unit and c ( w 1 , w 2 , 1) is the minimum cost of producing one unit. C) Verify that Shepherd’s lemma holds in this case. 2) There are two factors and the production function is F ( x 1 , x 2 ) = Max { x 1 a 1 , x 2 a 2 } A) Draw the unit isoquant in the x 1 , x 2 plane. B) Find x ( w 1 , w 2 , 1) and c ( w 1 , w 2 , 1). 3) There are two factors and the production function is F ( x 1 , x 2 ) = a 1 x 1 + a 2 x 2 . A) Draw the unit isoquant in the x 1 , x 2 plane. B) Calculate x ( w 1 , w 2 , 1) and c ( w 1 , w 2 , 1). 4) There are two factors and the production function is F ( x 1 , x 2 ) = x 1 / 2 1 x 1 / 2 2 . A) Calculate the ratio of the marginal products of factors 1 and 2. B) Calculate x ( w 1 , w 2 , 1) and c ( w 1 , w 2 , 1). C) Verify that Shepherd’s lemma holds in this case. 5) There are two factors and the production function is F ( x 1 , x 2 ) = 1 1 x 1 + 1 x 2 . A) Show that this is production belongs to the CES family. What is the

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Unformatted text preview: elasticity of substitution in this case? B) Calculate x ( w 1 , w 2 , 1) and c ( w 1 , w 2 , 1). 1 C) Suppose that a competitive ﬁrm faces the wages w 1 , w 2 ) for its inputs. How does the ratio of “factor shares” w 1 x 1 ( w 1 , w 2 , 1) w 2 x 2 ( w 1 , w 2 , 1) vary with the ratio w 1 /w 2 ? 5) There are two factors and the production function is F ( x 1 , x 2 ) = ± x 1 / 2 1 + x 1 / 2 2 ² 2 . A) Show that this is production belongs to the CES family. What is the elasticity of substitution in this case? B) Calculate x ( w 1 , w 2 , 1) and c ( w 1 , w 2 , 1). C) Suppose that a competitive ﬁrm faces the wages ( w 1 , w 2 ) for its inputs. How does the ratio of “factor shares” w 1 x 1 ( w 1 , w 2 , 1) w 2 x 2 ( w 1 , w 2 , 1) vary with the ratio w 1 /w 2 ? 2...
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prodprobs - elasticity of substitution in this case B...

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