In solow model of growth output per capita is function of
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Growth by capital accumulation
In addition to the production function, we need two other pieces of information:
the savings function -- how much of output do people in our model economy save? The simplest assumption (which we will examine in more detail later in the course, and will conclude can be a fairly good representation of people's behavior) is that people save a given fraction of output. For the sake of having a specific example, we assume that people save 1 / 4 of output, or what comes to the same thing, 25 cents for every dollar of income. The savings function is therefore:
s = 0.25 q
the equilibrium condition . We shall find that if capital accumulation is the only source of growth, the economy will approach an equilibrium orsteady state . It will reach the steady state when savings is just sufficient to replace the depreciated capital stock. If we assume that in each time period capital depreciates totally, theequilibrium condition is simply
s = k
Note that if depreciation were only 10 percent of capital stock, the equilibrium condition would be s = 0.10 k . Although this is a more realistic figure for yearly depreciation, we assume 100 percent depreciation for simplicity -- and if you are troubled by the lack of realism, you may think of our time periods as decades rather than years.
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In addition to the production function, we need two other pieces of information:
the savings function -- how much of output do people in our model economy save? The simplest assumption (which we will examine in more detail later in the course, and will conclude can be a fairly good representation of people's behavior) is that people save a given fraction of output. For the sake of having a specific example, we assume that people save 1 / 4 of output, or what comes to the same thing, 25 cents for every dollar of income. The savings function is therefore:
s = 0.25 q
the equilibrium condition . We shall find that if capital accumulation is the only source of growth, the economy will approach an equilibrium orsteady state . It will reach the steady state when savings is just sufficient to replace the depreciated capital stock. If we assume that in each time period capital depreciates totally, theequilibrium condition is simply
s = k
Note that if depreciation were only 10 percent of capital stock, the equilibrium condition would be s = 0.10 k . Although this is a more realistic figure for yearly depreciation, we assume 100 percent depreciation for simplicity -- and if you are troubled by the lack of realism, you may think of our time periods as decades rather than years.
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