Does anyone mind expaining the difference between a change in the function F and a change in TFP?

As shown below, “an innovation that makes it possible to produce the same output with the same amount of capital but fewer workers would be reflected in a change in the function F()” - I thought that an innovation that streamlined the operation of a machine, so that instead 2 workers operating it, only 1 is needed would be the result of an increase in TFP? Am I missing something here?

“It is worth noting that both the function F( ) and the scale factor A reflect technology. An innovation that makes it possible to produce the same output with the same amount of capital but fewer workers would be reflected in a change in the function F( ) because the relative productivity of labor and capital has been altered. In contrast, an increase in TFP does not affect the relative productivity of the inputs. As is standard in the analysis of economic growth, unless stated otherwise, the level of technology should be interpreted as referring to TFP” (CFA vol II, page 2.77)

The Cfa book paragraph is explaning 2 types of changes in the A*F(L,K) equation:

The first one is when there is an operative innovation so the proportion of L and K used has changed (I need fewer workers now to produce the same amount, which is better, it is cost optimizing), so this is a change in the F() equation only. This change can not be attributed to a change in the TFP.

The second one is a change in A (technology level). This factor is exogenous, so its effect on F() has not altered the proportion of use of L and K, but the effect here is an increased level of output of goods using the same amount of K and L. This case is actually an increase in TFP.

The Cliff Notes version is that TFP explains changes in output when the ratio of capital to labor is constant, while the function F explains changes in output when the ratio of capital to labor changes. In the article, TFP is illustrated by moving from one production curve to another, while F is illustrated by moving along a given production curve.

@S2000magician - your site is immensely helpful! Just a couple of quick questions if you have time…

In your diagram which shows an increase in technology, MPK>r which leads to higher investment in capital until MPK=r. Is it possible that MPK=r can be at a different amount? i.e. MPK may not be equal to 0.0625 (the original value of MPK)?

Secondly, if there is an innovation that increases the productivity of a machine, keeping the labour-to-capital ratio constant (2 workers and one machine) the machine now produces 10 units of output an hour instead of 9.

If the factory has no space for more additional capital to be added ( i.e. another machine), how can capital deepening occur after TFP has risen? Theory suggests investment in capital must occur to equalise MPK with r.

Apologies if these are stupid questions, I’m just having trouble visualising a real life siutation to aid my understanding.

According to neoclassical growth theory, the steady state occurs when MPK = r, where r is the cost of capital. So after a technology improvement, the only way that MPK would settle at some value other than its original value would be if the cost of capital changed.

Capital deepening can include buying additional factory space to add a new machine.

They’re not stupid questions. Understanding is what we’re after here.

Another question if you have time & a lot of patience!..

In the CFA material (vol II) Exhibit 14.Impact on the Steady State: Increase in the Saving Rate

An increase in the savings rate leads to higher k and y, however, it does not have an impact on the steady state growth rate of output per capital or output.

Does this mean, say for example, an economy is in the steady state growing at a constant rate of 2% per year. An increase in the savings rate pushes up output per capita so that in that particular year, growth was 3%. Thereafter, growth returns to 2% per year?