An increase in the saving rate would lead to a higher growth of output per

# An increase in the saving rate would lead to a higher

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An increase in the saving rate would lead to a higher growth of output per worker only for some time, and to a higher level of output per worker permanently. 21

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| faculty of economics and business 20-12-2016 How output and capital interact To determine output in the long run, two relations between output and capital should be noted: 1. The amount of capital determines the amount of output being produced. 2. The amount of output determines the amount of saving and, in turn, the amount of capital accumulated over time. 22
| faculty of economics and business 20-12-2016 The Solow growth model (3) To focus on the effect of capital accumulation on output, we make two simplifying assumptions: Population size, the participation rate and the unemployment rate are constant  employment N is constant. There is no technological progress ( A is constant, and set to 1). Using these assumptions, we can write: 23 K/N Y/N = f ( K/N ) Y/N Decreasing returns to capital per worker Y N f K N t t

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| faculty of economics and business 20-12-2016 The Solow growth model (4) To see how output and investment are related, we make the following assumptions. We assume the economy is closed: We assume public saving, T – G , is equal to zero. So We assume that private saving is proportional to income, that is Now, In per worker terms: 24 K/N Y/N = f ( K/N ) Y/N sf ( K/N ) S sY I s Y t t G T S I S I N Y s N I t t
| faculty of economics and business 20-12-2016 The Solow growth model (5) The evolution of the capital stock is given by: where denotes the rate of depreciation Using our assumptions (constant A and N ) above, this gives us: or: In words, the change in the capital stock per worker is equal to investment per worker (=saving per worker) minus depreciation per worker ( required investment ). 25 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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| faculty of economics and business 20-12-2016 The Solow growth model (6) The change in the capital stock per worker is equal to investment per worker (saving per worker) minus depreciation per worker ( required investment per worker ). 26 K/N Y/N = f ( K/N ) Y/N sf ( K/N ) δ ( K/N ) Change in capital per worker from year t to year t + 1 _ Depreciation per worker during year t _ = Investment per worker during year t = N K N K t t 1 N K t N K sf t
| faculty of economics and business 20-12-2016 Over time the capital stock per worker increases until we are in the steady state where: investment per worker (saving per worker) equals depreciation per worker ( required investment per worker ). 27 K*/N is the steady state level of capital per worker. K/N Y/N = f ( K/N ) Y/N sf ( K/N ) δ ( K/N ) K*/N Dynamics of capital and output (1)

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| faculty of economics and business 20-12-2016 Dynamics of capital and output (2) Since in the steady state the level of capital per worker remains unchanged, that is: we find: So, output per worker in the steady state is: 28 = 0 K N K N K N t t t 1 = s f K N t * * K K sf N N * * Y K f N N
| faculty of economics and business 20-12-2016 Dynamics of capital and output (3)

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