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Economics Dynamics Problems 156

# Economics Dynamics Problems 156 - 140 Economic Dynamics 14...

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140 Economic Dynamics 14. f 1 ( x ) and f 2 ( x ) are linearly dependent if and only if there exist constants b 1 and b 2 , not all zero, such that b 1 f 1 ( x ) + b 2 f 2 ( x ) = 0 for every x . If the set of functions is not linearly dependent, then f 1 ( x ) and f 2 ( x ) are linearly independent. Show that y 1 = Y and y 2 = tY are linearly independent. 15. Given the following version of the Solow model with labour augmenting technical progress Y t = F ( K t , A t L t ) K t + 1 = K t + δ K t S t = sY t I t = S t L t + 1 L t L t = n A t = γ t A 0 (i) show that ˆ k t + 1 = (1 δ ) ˆ k t + sf ( ˆ k t ) γ (1 + n ) where ˆ k is the capital/labour ratio measured in efficiency units , i.e., ˆ k = ( K / AL ) . (ii) Approximate this result around ˆ k > 0 . 16. Given the model q d t = a bp t b > 0 q s t = c + dp e t d > 0 p e t = p e t 1 λ ( p t 1 p e t 1 ) 0 < λ < 1 (i) Show that price conforms to a first-order nonhomogeneous differ- ence equation.
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