In a traditional Solow-Swan growth model, you can decompose growth in labor productivity (output/hour) into a component stemming from total factor productivity growth and another stemming from capital deepening (increases in the capital/worker ratio).
Let's assume that I create a new machine which doubles the output of soybean production and try to sell it to soybean farmers. Prior to adopting my machine, farmers used horses and primitive plows to grow their soybeans. From the perspective of the farmer, after buying my machine and using it, they work the same amount, but they produce 2x as much, so their labor productivity has doubled. However, to what would you attribute the growth in output? Would you attribute it to capital deepening (because the farmer is now using more capital than before), or total factor productivity?
The reason I ask is because total factor productivity growth is generally considered by economists to be a measure of "the pace of technological progress" (See: The Rise and Fall of American Growth and other books of the same nature). But the act of creating my fancy soybean picking machine was in of itself a technological act. I had to combine some other capital inputs (steel, etc.) and some labor (my own and perhaps my employees) with insight to create the machine in the first place. I'm a bit confused about the growth accounting here.
A follow up question makes the situation a bit harder. Let's say that again I have invented a new machine tool. This machine tool let's car makers make smooth surfaces that are more aerodynamic and look cooler. This improves the look and miles/gallon figure of cars made using my machine tool. Car companies realize that consumers' are going to love the new look and higher MPG of cars made with the machine, so they purchase it in droves. In this situation, would labor productivity (output/hour) or even raw output of cars increase? After all, nothing has changed about the fundamental efficiency of producing the car - if anything the cost of producing the car has gone up because the fixed costs the car manufacturer pays to buy my machine must now be amortized over every car they sell. If the former did rise, would you attribute it to capital deepening - the car OEM is using more capital than before - or total factor productivity?