Why firms need innovation? A simple explanation using Solow's growth model

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Solow's growth model was developed originally to explain national-level growth mechanism, but it also provides a nice theoretical framework on micro-level to explain why firm needs innovation.

Suppose a firm's output is decided by the production funtion Y=AF(K,L). A is ideas or productivity, K is physical capital (e.g. factories, truck) and L is labor. If we draw a graph between Y and K (or L), it should roughly like this:

When a firm buys its first new truck, the incremental value on output Y is huge. But as it buys more and more trucks, controling all other factors the same, the change in Y becomes smaller. This rationale can also be applied to labor investment.

Now suppose the firm invest 30% of its output to buy new capital. This is indeed what's happening in the economy where firms re-invest its profit into new production equipment or hiring new employees etc. If these investment doesn't depreciate, we can imagine that this firm can grow forever through: production of Y -> investment of Y into new K -> higher K gives higher level of Y. Though the growth level decreases, the firm will continue growing.

But in reality, both K or L depreciates. Trucks may not work any more after 10 years of serving time; employees can become less productive when they growth older. Thus, a certain portion of the investment must be used to cover this depreciation.

Suppose depreciation equals to 2% of the current level of capital. From the graph below, when can see that in the initial period, investment in capital > depreciation. Thus, the firm is still accumulating capital, thus Y increases. However, at the point where investment = depreciation, K no longer grows. The firm's capital level stagnates and output stops growing.

So how can this firm continue its growth? One solution is to raise investment rate. This pushes the investment line upward and increases the equilibrium capital level, resulting in higher level of output. But this approach has its limitation.

First, investment rate can at most be 100%. This is the case of some growth-stage companies which don't pay dividend at all, but instead put all its profit into re-investment. With 100% investment rate, it's still guaranteed that the firm will reach its equilibrium capital level one day.

Second, shareholders want to get their dividend. Firms need to repay the investment of their shareholders to keep them happy.

Third, there may not be that many investment opportunities out there. Increasing investment for its own sake can leads to unprofitable investment choices.

This is where innovation comes to play as a sustainable source for long run output growth. Innovation is essentially measured by the variable A in the production function Y = AF(K,L). An example of it can be "corporate culture". Given a fixed level of K and L, a firm with good corporate culture can be much more productive than the one without it.

When a firm is doing this sort of innovation, "A" increases and the output line is pushing upward. As a result, the investment line is also pushing upward and thus increasing the equilibrium level of capital. The firm can grow again! What's more importantly is that this process can be continue forever, unlike the limitation of investment rate. Firms can always find new ideas to make labor and capital more efficient, as demonstrated by the history of private enterprises.

This explains why firm needs innovation. Without innovation, the growth relying on increasing the level of K and L is destinied to stop at some point of time. Increasing investment rate can help, but it's only a temporary solution. What ensures long run growth of the firm is always its power to innovate, finding new ideas to make the production more efficient.

© Zhiwei (Berry) Wang.RSS