ps1325f2009 - Prove that F is homogeneous of degree one if...

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Professor M. Alexopoulos Department of Economics 150 St. George St. Rm: 205, Tel: 978-4962 email: malex@chass.utoronto.ca ECO325F: Advanced Economic Theory-Macro Problem Set #1 1. Which of this gross production functions generally display constant returns to scale in labour and capital (i.e. if K and L double, does Y double)? For those that do not display constant returns to scale for all parameter values, find the parameter values that make them satisfy constant returns to scale. a. ln Y A ln K ln L (Cobb-Douglas) b. Y A min K , L (Leontieff) c. ln Y A B ln 0 K 1 L (CES) d. ln Y A 0 ln K 1 ln L 1 2 3 ln K 2 2 4 ln K ln L 5 ln L 2 (Translog) e. Y A 0 K 1 L (Linear) 2. Let F K , L G K , L H K , L . a.
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Unformatted text preview: Prove that F is homogeneous of degree one if both G and H are. b. Give a counter-example to show that the fact F is homogeneous of degree one does not always imply that G and H are homogeneous of degree one. c. Let H K , L L . Prove that F is homogeneous of degree one iff G is also homogeneous of degree one. 3. Romer 1.1 4. Romer 1.2 Assume in this question that during the time t 1 to t 2 that the growth rate increases linearly from 0 to a . 5. Mathmatically describe the function X t in Romer 1.2. Hint: What is the growth rate of the function Y t e b 2 t 2 ?...
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ps1325f2009 - Prove that F is homogeneous of degree one if...

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