9. Balanced growth is experienced when all variables are increasing at the same proportional rate. Balanced growth demands that all variables involved in the model must increase the same constant proportion. FEATURES OF SOLOW MODEL In Solow model, aggregate production function has been taken on some assumptions. It is assumed that a composite goods is produced by using a technology which is same for all firms. It further assumes that factor inputs of labour and capital are homogeneous. Let us explain in detail how in this model demand for and supply of goods is determined.
Supply of Goods: Solow model determines the supply of goods on the basis of production function. The production function has three inputs ( k, l, A) and one output (Y) variables and takes the form Y ( t ) = F ( k(t) , A ( t ), L ( t ), ...(i) where Y refers to income or output k is capital L is labour and t is technology of production. t is time. Since ‘ t ’ is not entering the model directly, it implies that over time change in Y will take place only due to change in inputs k, l and A. It is important to note that ‘A’ which is referring to technology of production will change over time. It is further important that labour and effectiveness of labours have been taken as multiplicatively such that AL means effective labour. It implies that technological progress increases the productivity or efficiency of labour. It means that even if the quantity of labour remains unchanged, technological progress increases efficiency of labours thereby quntity of effective labour (AL). The production function given in eqn. (i) is representing constant returns to scale constant returns to scale are said to exist when inputs and output change in the same proportion i.e. double the inputs, output will get doubled. F ( a k, a AL) = a F ( k, AL) ...(ii) We can use this assunption to convert the production function given in eqn. – (i) to per-effective labour terms. If a = (i) 1 AL , eqn. (i) can be written as 1 F .| ( ,AL) AL AL k f k ...(iii) Such a production function is called production function of intensive form. It helps us to analyse all variables in the economy relative to the size of effective labour force. Therefore, AL k is capital per effective labour unit. Moreover, Y F AL AL k and Y AL is output per effective labour unit.
In the figure above we have taken K/Al i.e. capital per unit of effective labour or x- axis, and Y/AL i.e. output per unit of effective labour on y -axis. It is clear from the diagram that if both labour and capital are increased in the same proportion. Constant returns to scale prevail but if only capital is increased keeping AL constant, we shall get diminishing returns to capital. The marginal productivity of capital is determined by the slope of production function. MPK is equal to extra output per effective labour produced when AL k is increased by 1 unit Symbolically, MPK = f (k + 1 ) – f (k) . ...(iv) The intensive form of production function given in eqn. ( iii) is assumed to satisfy following conditions: 1. at k = 0, f (k) = f ( 0 ) = 0 (b) When f' (k) > 0, MPK is positive (c) When f" (k) < 0, MPK declines.
- Winter '17