Summary Decreasing the cost of a factor of production creates an overhang if the elasticity of substitution between factors is less than 1 This corresponds to whether or not the elements of the production function are substitutes or complements - if you have a good enough algorithm does it not matter really how much compute and data you have, or does that algorithm get better performance the more compute and data you have?
Thank you for sharing this post. I found the definition of "overhang" helpful. I have a question about this production function example.
I think the example production function that is more productive for resource "a" should be written like this, "If we make a twice as productive the production function now looks like y=min{2a,b} ... " instead of "y=min{a/2,b}"
Do you agree with this? I wrote out an example below to clarify my understanding.
Let's say we're making bicycles and "a" represents wheels while "b" represents bike frames.
From my point of view, if we require two wheels and one frame to make one bicycle of output (denoted y), our production function would be y = min { a / 2, b }
This means, for example, if we have ten bike frames and six wheels, we could only produce min { 6 / 2, 10 } = min { 3, 10 } = 3 bikes
In this scenario, we could make our factory more productive over wheels by switching from making bicycles to making unicycles (assuming we can sell both bicycles and unicycles for a similar same price, demand for both is consistent, etc.)
In this situation, our production function now becomes more efficient in terms of a so y = min { a, b }
However, assuming consistent demand and price, we would also be incentivized to use more bike frames in this scenario. If we still have ten bike frames and six wheels, now our total productivity is six unicycles but we are consuming six bike frames as well.
Thank you for sharing this post. I found the definition of "overhang" helpful. I have a question about this production function example.
I think the example production function that is more productive for resource "a" should be written like this, "If we make a twice as productive the production function now looks like y=min{2a,b} ... " instead of "y=min{a/2,b}"
Do you agree with this? I wrote out an example below to clarify my understanding.
Let's say we're making bicycles and "a" represents wheels while "b" represents bike frames.
From my point of view, if we require two wheels and one frame to make one bicycle of output (denoted y), our production function would be y = min { a / 2, b }
This means, for example, if we have ten bike frames and six wheels, we could only produce min { 6 / 2, 10 } = min { 3, 10 } = 3 bikes
In this scenario, we could make our factory more productive over wheels by switching from making bicycles to making unicycles (assuming we can sell both bicycles and unicycles for a similar same price, demand for both is consistent, etc.)
In this situation, our production function now becomes more efficient in terms of a so y = min { a, b }
However, assuming consistent demand and price, we would also be incentivized to use more bike frames in this scenario. If we still have ten bike frames and six wheels, now our total productivity is six unicycles but we are consuming six bike frames as well.