no government ie public saving TG 0 private saving is proportional to income so

# No government ie public saving tg 0 private saving is

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“no government”, i.e., public saving, T–G = 0 . private saving is proportional to income, so Combining gives: 8 S sY I s Y t t

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| Date 09-01-2017 faculty of economics and business Let us verify 9
| Date 09-01-2017 faculty of economics and business Memory refreshment (wk 6) The evolution of the capital stock is given by: Where: denotes the rate of depreciation Using our assumptions above, this gives us: Or: In words, the change in the capital stock per worker (left side) is equal to saving per worker minus depreciation (right side). 10 K K I t t t 1 1 ( ) K N K N s Y N t t t 1 1 ( ) K N K N s Y N K N t t t t 1

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| Date 09-01-2017 faculty of economics and business Memory refreshment (wk 6) 11 Change in capital from year t to year t + 1 _ Depreciation during year t _ = Investment during year t = From our main relations above, we express output per worker ( Y t / N ) in terms of capital per worker, to derive the equation below: N K N K t t 1 N K t N K sf t Y N f K N t t K N K N s Y N K N t t t t 1
| Date 09-01-2017 faculty of economics and business The steady state 12

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| Date 09-01-2017 faculty of economics and business Labor and effective labor (1) How should we interpret this production function: Output depends on both capital and labour ( K and N ), and on the state of technology ( A ). Output depends on capital ( K ) and effective labor ( AN ). Both interpretations are correct. However, the second one turns out to be very convenient. 13 Y F K A N ( , )
| Date 09-01-2017 faculty of economics and business Labor and effective labor (2) Technological progress increases AN, i.e., the amount of effective labor a.k.a. labor in efficiency units. With constant returns to scale: Or more generally: 14 2 (2 ,2 ) Y F K AN ( , ) xY F xK xAN

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| Date 09-01-2017 faculty of economics and business A Solow model deja vu!? Based on the notion of effective labour (instead of labor, we can repeat the steps of the previous chapter: The relation between output per effective worker and capital per effective worker is: Redefined as: 15 , 1 Y K F AN AN Y K f AN AN
| Date 09-01-2017 faculty of economics and business Output and capital per effective worker 16

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| Date 09-01-2017 faculty of economics and business Dynamics of output and capital To arrive at the steady state, we can redo all steps of last week. However, we should now do all steps per effective worker. Question: What does it mean when the economy is in the steady state?
• Fall '17
• Economics, 2 K, 1 K, 0 k, dr. R.M. Jong-A-Pin

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