Question

Use a Solow-Swan diagram to show the qualitative effects of this increase in savings rate upon steady state output per worker and capital per worker. Briefly describe the intuition behind this result.

Answer 1

Answer :

Solow’s classic model is a superb piece of work, everything you could ask of a theory. It takes on the biggest questions e.g., what determines standards of living, why some countries are rich and others poor. The argument is based on standard assumptions, yet it arrives at not-at-all obvious implications. It fits the facts well. So much so that Solow’s model sets the framework for all serious empirical studies of growth and productivity. Solow highlights technical change i.e. productivity growth as the key to long-run growth of per capita income and output. Accumulation of capital creates growth in the long run only to the extent that it embodies improved technology.

k* is the steady state level of capital per worker and Y* is the steady state level of output - the long-run equilibrium of the economy.

Now lets analyse the impact of increase in savings rate : Due to increase in savings rate, investment will increase which will shift the investment curve to the right as shown in the figure 2 below. The new equilibrium level of capital will be k₁* and the new equilibrium level of output will be  Y₁* as shown in the figiure below.

The capital stock rises eventually to a new steady state equilibrium, at k₁*. During the transition output as well as capital grows, both at a diminishing rate. Growth tapers off to nothing in the new steady state

Implications: A permanent increase in the saving ratio will raise the level of output permanently, but not its rate of growth. During the transition period, which might last decades, growth will be higher. But the increased investment eventually results in an offsetting increase in depreciation, and hence capital per worker levels off. Saving and capital accumulation on its own, with given technology, cannot explain long-run economic expansion.

Golden rule: The equilibrium value of capital per effective worker increases with the saving ratio. In steady state, the per capita income path is higher for a greater savings ratio. Is more saving always better? No. We want to maximize consumption, not income. A greater capital stock requires more break-even investment—i.e. investment just to keep capital per effective worker constant. At some point, because of decreasing MPK, capital increases start to cannibalize capital itself, at the margin leaving nothing for consumption.

To maximize consumption, we want to hold the capital ratio at the point where further increases in capital cease to yield a marginal gain in consumption. This point in Figure 3.8 is G. Beyond that point increases in capital per effective worker create decreases in consumption, despite continued increases in output. The Golden Rule describes the consumption-maximizing path of capital accumulation corresponding to G. As a matter of geometry, at G the slope of the production function (the gross marginal product of capital) is equal to the slope of the break-even line. That is:

MPK = δ + n + g or

MPK - δ = n + g.

Under the Golden Rule, the net marginal product of capital is equal to the growth rate of total output.

Real interest and growth rates In equilibrium, the interest rate (the return on saving) is equal to the net marginal product of capital after depreciation. If the interest rate is less than the growth rate, the economy is saving too much—i.e. consuming more provides a free lunch.

An efficient economy therefore would have the long-run equilibrium real rate of interest (or natural rate) equal to, or above, the growth rate. The Golden Rule has equality.

To apply this to the real world one has to recognize that

• actual interest rates are many and varied, with different terms and risks and other features, depending on the asset and the borrower
• returns on capital may be highly uncertain, and therefore contain a risk premium over and above the interest rate on financial assets

Bearing in mind these qualifications, one can say that if the economy is operating efficiently, then in the long run the real yield on long-term government bonds (creditrisk-free assets) should be about equal, or slightly above, the growth rate.

Evidence : The US has a very large budget deficit, about 5% of GDP, for as far as the eye can see, with the Administration offering more tax cuts, and some high-priced new programs (medicine for seniors, Americans on Mars,). Budget deficits reduce national savings, which might not be too bad if the private saving rate were high, but in the US it is low. The Solow model warns that such a policy is likely to reduce income growth over an extended period