## The difference between Solow and Harrod-Domar

The Harrod-Domar model is a good starting model for thinking about growth. It is based on a few key concepts:

Capital accumulation – growth comes from increasing a country’s productive capacity, it does this by increasing its capital stock. The economy adds to its capital stock through firms investing in new capital, it loses capital stock through depreciation (existing capital wearing out). As long as there is more investment going on than depreciation, capital stock increases and so does the productive capacity of the economy.

The saving rate – national income is either consumed now or saved for the future. The more households are saving now, the more loanable funds are available for firms to access to finance their investment. So the more saving going on, the more investment is possible. Hence saving is key to increasing the productive capacity of the economy and so key for growth.

The capital-output ratio – the efficiency of the economy at using capital to produce output. This is a kind of measure of the quality of the capital the country is using, a low capital-output ratio means the economy is efficient, it can produce a lot of output from a given amount of capital, but a high capital-output ratio implies it does not get much output from a given amount of capital.

This last point, the capital-output ratio, is the contentious part of Harrod-Domar. It is stretching it a bit to assume that the capital-output ratio stays fixed, because in the real world there is not just one factor of production (capital), the capital needs labour to operate, so we have to take into account a second factor (labour). If you keep increasing the amount of capital faster than the labour force grows, then there will be less people available to use each unit of capital, so it is not really reasonable to assume that adding another unit of capital will give you as much of an increase in output as it did when you had less capital. It’s the same principle as the diminishing returns to factor in firms, if a firm used two inputs, people and machines, and it had say 100 people and 50 machines, and produced 1000 units of output, then that means 2 people per machine and a capital-output ratio of 0.05. If you kept the workforce fixed at 100 and multiplied the capital by 10, so you had 500 machines, you would now have only 0.2 people to work each machine. So the odds are you wouldn’t multiply your output by 10 to 10000. You might reasonably expect output to have increased but not by that much. If output ended up at say 4000 then you would have a new capital-output ratio of 0.125. So the capital-output ratio would be rising.

This is what tends to happen with capital accumulation in the context of a national economy. As you increase capital above the rate of increase of population, the capital-output ratio rises. So instead of being a straight line, the production function will be curved:

The black curve is the production function, this shows how much output per worker (Y/N on the vertical axis) you get for the amount of capital per worker (K/N on the horizontal axis) you have. The red and blue lines pick out amounts of output you get for particular amounts of capital. Notice that by adding a lot more capital from red to blue, you don’t get quite so much of an increase in output. The angle of the two lines basically shows you the capital-output ratio, when you go from red to blue, the angle drops meaning you are getting a higher capital-output ratio as you increase capital.

The Solow model basically takes into account the fact that there will be **diminishing returns to capital** as you keep increasing it. But the other principles of the Harrod-Domar model, growth coming through capital accumulation, and the saving rate influencing capital accumulation, stay in the Solow model, so if you understand Harrod-Domar it is fairly easy to pick up Solow.