Published on August 3, 2014
The Solow Growth Model (Solow and swan): The Solow Growth Model (Solow and swan ) Presented by Ganga Pd. Khanal MBA, 2 nd Semester. Introduction: Introduction This model was developed by SOLOW and SWAN in 1956. This model is a model of capital accumulation in a pure production economy. This model was awarded by NOVEL PRICE in 1967. -Wildly used in policy making -Benchmark for other growth model -Economic growth in long run Assumption: Assumption There is exists aggregate production function Two factor input( ie . Labor and Capital) Both Capital and Labor are significant Marginal productivity is positive but diminishing Production function characterizes CRS Imperfect rate of substitution between capital and labor Technology is given Some technical term: Some technical term Term Aggregate (Symbol) Per capita (symbol) Total output= Real income=GDP Capital stock Population Size(labor supply, all everyone works) Consumption Saving Investment Y K P C S I y (Y/L) k (K/L) p c (C/Y) i (I/L) Derivation of Solow model : Derivation of Solow model Aggregate Production function Y = F(K,L) For per capita production function, Or,Y /L=F(K/L, L/L)] Or, y=f(k) (per capita output depends upon per capita capital) : → …………………( i ) y=f(k) PowerPoint Presentation: National Income Identity Total consumption and Investment shows the total national Income Y =C+I For per capita output Or, y= c+i Consumption depends upon income Or, c = y- i Or, c=(1-s)y : → …………………(ii) Where s= saving rate ( saving rate is in between o and 1) c= (1-s)y PowerPoint Presentation: Where, (1-s) =b=marginal propensity to consume From equation (ii) Saving= y-(l-s)y Or, Saving =y- y+sy Or, saving= sy We know, In equilibrium saving=investment( ie . s= i ) Therefore, i =s Or i = sy We know, y=f(k) → from equating ( i ) Or, i = sf (k) : → …………………(iii) i = sf (k) PowerPoint Presentation: The steady state In steady state, growth rate is zero. ∆k = sf (k)-( d+n )k=o Or, sf (k*)= ( d+n )k* : → …………………(ii), which is know as fundamental equation of Solow model. Where, * Indicates steady state values. Larger amount of investment are required to maintain ∆k =0. The economy will always work itself to a steady state point. if rate of capital replenishment is greater than the loss due to depreciation and population growth ,( sf (k)>( d+n )k, then the capital stock will shrink. sf (k*) = ( d+n )k* PowerPoint Presentation: Fig: The steady state in a Solow growth model with depreciation and population. Higher the saving rate , the higher the capital per worker and higher the output per worker. PowerPoint Presentation: The Golden Rule The steady state associated with particular outcome is called “GOLDEN RULE” (GR) steady state. We know, .y= c+i Or,c+I =y Or, c = y-I, i = ( d+n )k* Or, c*=f(k*)-( d+n )k* Higher the level of capital mean higher level of output. They also mean more capital is being removed from economy each year. The GR steady state occurs when f ’(k*) = ( d+n )k* : → …………………(iv), Where, f’(k*)=MPK f ’(k*) = ( d+n )k* PowerPoint Presentation: Fig:of the GOLDEN RULE steady state- The dotted line represent the slope of the production function at the equilibrium points and the subscripts “GR” indicates values are Golden Rule steady state. PowerPoint Presentation: If the MPK is greater than ( d+n ), we know that adding capital will increase consumption . When MPK is less than ( d+n ), Decreasing capital will increase consumption . Maximization of consumption occurs when eq (iv) holds. A planner trying to maximize long run consumption would then aim to get a saving rate that corresponded that particular steady state level of capital. Role of saving in economic growth Increase in saving leads to higher per capita capital and per capita output. But change in saving leads to lower income level to higher income level. It does not guarantee higher economic growth for lung run. Role of population growth Population growth decreases the per capital output and capital. PowerPoint Presentation: Conclusion The Solow model predicts growth is always positive, but slowly declines to zero. Economic with a high population growth rate can never take over. The Solow model does currently predicts that higher population growth rates and lower saving investment rate are with lover levels and lower standard of living. Solow model states that at steady state economic growth rate is zero. Economic growth rate converses at higher level . Growth rate slows down of higher income counties. PowerPoint Presentation: THANK YOU for your attention….