# A steady state is a situation in which the economys

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A steady-state is a situation in which the economy’s output per worker, and capital per worker are constant Y is growing in line with N - K is growing in line with N No variable is getting out of line with regard to any of the others. – there is a sustained growth in Y Therefore output and capital stock expand precisely in line with population growth. In such balanced growth situation, K/Y remains constant There is aggregate growth (Y), but not per capita growth (Y/N). Solow found that: For a given set of conditions and parameters, there is only one balanced growth point Any point on the TP curve that is not a balanced growth point cannot be kept going in the long run. Economy is always pulled towards a balanced growth point. Conditions for a balanced growth point
Is there specific conditions under which Y/N and K/N will be constant? –when economy would remain stationary at point on TP o Stationary point on TP means, if the population is growing at a rate n , Y and K must also grow at a rate n in order for Y/N and K/N to be constant. Conditions for such a situation: o K must grow at the same rate as N, e.g. at a rate of n . – each additional worker must get average amount of capital per worker o Capital stock normally depreciates (wear and tear) year by year and therefore the depreciation must also be replaced to keep K/N constant. Depreciated capital stock = δK t (δ – rate of depreciation). The required investment per worker for K to keep up with the growth in N (K/N constant): o I t / N t = δK t /N t + nK t /N t o I t / N t = (δ + n) K t /N t (BL 319) = the required investment per worker to keep K/N and Y/N stable. Not all these values may be feasible – there may be insufficient investment in economy Because Investment needs to be financed from savings. Savings is the proportion of total income that is not spent on consumption. Savings in year t: o S t = s Y t s is the average savings rate All savings ends up in some form of investment In other words: Total actual investment is = to total savings - Therefore : I = S Thus actual, available investment is: I t = sY t Or in Actual investment per worker terms: I t /N t = s (Y t /N t ) In stable / equilibruim situation – actual investment per worker will match the required investment per worker The condition for the stable/ equilibrium situation must be: o actual investment per worker = required investment per worker o s (Y t /N t ) = (δ + n) K t /N t o This is the condition for the balanced growth point / steady state on the TP curve. o The condition is not met – increase / decrease in capital per worker (K/N) – economy will not be stationary on TP Graphically: expression on left and right hand side of balanced growth conditions can be shown in Figure 8.4 Actual investment = s (Y t /N t ) It is a Proportion (e.g. s = 10%) of the TP curve (same shape, just under the TP curve) Required investment = (δ + n) K t /N t Straight line through the origin of the diagram with a slope of (δ + n) Stable vale of K 0 /N 0 is at intersection of two curves Corresponding stable/balanced growth level of Y/N
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