homework1 2009_final version

homework1 2009_final version - wage is L t L t A t K F t w...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ECN/APEC 6000/7230 Fall 2009 Homework 1 Due 9/8/09 1) Show the following properties of the growth rates of positive variables (i.e dt t dX t X ) ( ) ( 1 for a variable X ( t ). a) The growth rate of the product of two positive variables is the sum of their products: . ) ( ) ( 1 ) ( ) ( 1 )) ( ) ( ( ) ( ) ( 1 dt t dY t Y dt t dX t X dt t Y t X d t Y t X + = b) The growth rate of the ratio of two positive variables is the difference in their growth rates: . ) ( ) ( 1 ) ( ) ( 1 ) ( ) ( ) ( ) ( dt t dY t Y dt t dX t X t Y t X dt d t X t Y - = c) The growth rate of a positive variable raised to the α power is times the growth rate: . ) ( ) ( 1 )) ( ( ) ( 1 dt t dX t X dt t X d t X = 2) Suppose that labor and capital are both paid their marginal products, so the real
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: wage is L t L t A t K F t w = )) ( ) ( ), ( ( ) ( and the rate of return on capital is . )) ( ) ( ), ( ( ) ( - = K t L t A t K F t r a) Show that if F exhibits constant returns to scale then ECN/APEC 6000/7230 Fall 2009 ))]. ( ( ' ) ( )) ( ( )[ ( ) ( t k f t k t k f t A t w-= b) Show that if F exhibits constant returns to scale then ), ( ) ( ) ) ( ( ) ( ) ( t Y t K t r t L t w = + + so the sum of factor payments equals net output....
View Full Document

Page1 / 2

homework1 2009_final version - wage is L t L t A t K F t w...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online