THE HARROD-DOMAR MODEL
It assumes that the aggregate production function has fixed technological coefficient:
Y = F(K, L) = min{AK, BL}
where A and B are the fixed coefficients. Under this technology, producing a unit of output requires 1/A units of capital and 1/B units of labour, if either input falls short of this minimum requirement, there is no way to compensate by substituting the other input.
When AK< BL, (this is the case which is emphasised)
Y = AK ……………………(1)
With a fixed saving rate, capital stock will grow according to the same equation as in neoclassical model.
From equation 1 and 2 we get
So the growth rate of capital is given as,
Because output is strictly proportional to capital, g will also be the rate of growth of output. It follows immediately that the growth rate of output is increasing in the saving rate s.
The problem with the Harrod-Domar model is that it cannot account for the sustained growth in output per person that has taken place in the world economy since the industrial revolution.
A Neoclassical Version of Harrod-Domar (Frankel learning by doing model)
As in Harrod-Domar, the model would generate a long-run growth rate that depends on the saving rate. Frankel built his model on the foundation of learning by doing. He recognized that because individual firms contribute to the accumulation of technological knowledge when they accumulate capital, the AK structure of the Harrod-Domar model does not require fixed coefficients.
Instead, he assumed that each firm j belongs to {1, 2, . . . , N} has a production function of the form
Where kj and Lj are the firm’s own employment of capital and labour, and A is (aggregate) productivity. Aggregate productivity in turn depends upon the total amount of capital that has been accumulated by all firms.
where η is a positive exponent that reflects the extent of the knowledge externalities generated among firms.
For simplicity assume that
Since all firms face the same technology and the same factor prices, they will hire factors in the same proportions, so that
The model is then closed by assuming a constant saving rate, which generates
the same capital accumulation as in Solow-Swan and Harrod-Domar. Using the output equation to substitute for Y in this equation we have
To analyse the dynamic path of the economy we take three cases
Case 1. α+η<1
In this case the extent of knowledge spillovers η is not sufficiently strong to counteract the effect 1 -α of decreasing returns to individual capital accumulation, and the long-run growth rate is zero. It produces the same aggregate dynamics as the Solow-Swan model with no technological progress and no population growth. there is a steady-state capital stock at which the growth rate gK of capital is zero,
Case 2. α+η > 1
In this case learning externalities are so strong that the aggregate economy experiences an ever-increasing growth rate. That is, again equation 9 defines a unique steady-state capital stock but it is no longer stable, because growth rate of capital (gK) is now an increasing function of K, so that if K were to rise above K* it would keep on rising, at an ever-increasing rate. This is known as the explosive growth case.
Case 3. α+η =1
Thus the aggregate growth becomes
Which states that, as capital increases, output increases in proportion, even though there is continual full employment of labour and even though there is substitutability in the aggregate production function, because knowledge automatically increases by just the right amount. (which is equal to Harrod-Domar growth rate).
Reference: Aghion & Howitt.
It assumes that the aggregate production function has fixed technological coefficient:
Y = F(K, L) = min{AK, BL}
where A and B are the fixed coefficients. Under this technology, producing a unit of output requires 1/A units of capital and 1/B units of labour, if either input falls short of this minimum requirement, there is no way to compensate by substituting the other input.
When AK< BL, (this is the case which is emphasised)
Y = AK ……………………(1)
With a fixed saving rate, capital stock will grow according to the same equation as in neoclassical model.
From equation 1 and 2 we get
So the growth rate of capital is given as,
Because output is strictly proportional to capital, g will also be the rate of growth of output. It follows immediately that the growth rate of output is increasing in the saving rate s.
The problem with the Harrod-Domar model is that it cannot account for the sustained growth in output per person that has taken place in the world economy since the industrial revolution.
A Neoclassical Version of Harrod-Domar (Frankel learning by doing model)
As in Harrod-Domar, the model would generate a long-run growth rate that depends on the saving rate. Frankel built his model on the foundation of learning by doing. He recognized that because individual firms contribute to the accumulation of technological knowledge when they accumulate capital, the AK structure of the Harrod-Domar model does not require fixed coefficients.
Instead, he assumed that each firm j belongs to {1, 2, . . . , N} has a production function of the form
Where kj and Lj are the firm’s own employment of capital and labour, and A is (aggregate) productivity. Aggregate productivity in turn depends upon the total amount of capital that has been accumulated by all firms.
where η is a positive exponent that reflects the extent of the knowledge externalities generated among firms.
For simplicity assume that
Since all firms face the same technology and the same factor prices, they will hire factors in the same proportions, so that
The model is then closed by assuming a constant saving rate, which generates
the same capital accumulation as in Solow-Swan and Harrod-Domar. Using the output equation to substitute for Y in this equation we have
To analyse the dynamic path of the economy we take three cases
Case 1. α+η<1
In this case the extent of knowledge spillovers η is not sufficiently strong to counteract the effect 1 -α of decreasing returns to individual capital accumulation, and the long-run growth rate is zero. It produces the same aggregate dynamics as the Solow-Swan model with no technological progress and no population growth. there is a steady-state capital stock at which the growth rate gK of capital is zero,
Case 2. α+η > 1
In this case learning externalities are so strong that the aggregate economy experiences an ever-increasing growth rate. That is, again equation 9 defines a unique steady-state capital stock but it is no longer stable, because growth rate of capital (gK) is now an increasing function of K, so that if K were to rise above K* it would keep on rising, at an ever-increasing rate. This is known as the explosive growth case.
Case 3. α+η =1
Thus the aggregate growth becomes
Which states that, as capital increases, output increases in proportion, even though there is continual full employment of labour and even though there is substitutability in the aggregate production function, because knowledge automatically increases by just the right amount. (which is equal to Harrod-Domar growth rate).
Reference: Aghion & Howitt.
Hi. I’m Vivek Sharma. I do write Blog on different issues and topics related to Economy, Exams and Political issues. Inspired to make things looks better.
0 comments:
Post a Comment