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# ch3notes - An Overview of Economic Growth U.S standards of...

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An Overview of Economic Growth U.S. standards of living are vastly superior to 100 years ago. Higher incomes. Many new products. Better Health. More Education. But this explosion in living standards is a new phenomenon. Standards of living vary considerably in different countries. Some poorer countries seem to catch up. Other poorer countries continue to lag behind. We seek to explain growth in incomes over time. We seek to explain differences in countries’ standards of living.

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The History of Economic Growth
The U.S. Growth Experience

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Growth Rates Definition: t t t y y y g - + 1 Alternatively, t t t t t y g y y g y y ) 1 ( 1 1 + = = - + +
A quantity growing at a constant rate, g , follows: t t t t y g y g g y g y 2 1 2 ) 1 ( ) 1 )( 1 ( ) 1 ( + = + + = + = + + In general: 0 ) 1 ( y g y t t + =

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Doubling Time Time for 0 y to grow to 0 2 y Solve for t: ( 29 ) 1 ln( ) 2 ln( ) 1 ln( ) 1 ( ln ) 2 ln( ) 1 ( 2 ) 1 ( 2 0 0 g t t g g g y g y t t t + = × + = + = + = + = For small g , g g + ) 1 ln( , and so: Rule of 70: percents) in ( 70 7 . 0 ) 2 ln( g g g t =
Logarithmic Scales ) ln( ) 2 ln( ) 2 ln( ) 4 ln( ) 4 ln( ) 8 ln( y y y y y y - = - = - ln( y ) ln(2 y ) t Log of y ln(4 y ) ln(8 y )

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Ratio Scale Vertical Axis identified as the level of y . Spacing is the same as a logarithmic scale. 1 2 4 8 t y
Intercept and Slope of Ratio Scale ( 29 t g y t g y y g y y g y t t t t +

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