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PPF of our country is based on potential the most efficient use of our resources, NOT their actual use. The problem is, it's unclear for me how to estimate said potential. How to know where potentiality ends and impossibility begins? Not necessarily with clean-cut distinction, a rule of thumb can be good enough too.

Examples:

  • (An increase of productivity needs a cultural shift) Maybe we would be able to increase production by increasing participation of women in the workforce, but our culture CURRENTLY dictates that married women should NOT work. So would our PPF include increased production caused by by cultural shift? Or would we experience an increase of PPF?

  • (An increase of productivity needs a political shift) Maybe our production would increase if we used these sweet new technologies. But alas, we can't have them due to sanctions and it would require radical change in our current political regime in order to have possibility for sanctions being lifted. If sanctions were lifted after revolution would it mean that our PPF increased or that we got closer to it?

  • Maybe our production would increase if we used industrial espionage to get new technologies, but such secret operations have very high possibility of a complete failrue. Would success mean that we increased our PPF?

  • Maybe our production would increase if there was industrialization in our society. But our society have never been industrialized in the first place. And it would take many years and lots of efforts to industrialize it.

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You can estimate the PPF just by technically estimating what’s the production function for all goods and what’s the resource constraint.

For example, let’s for the sake of simplicity assume that the only factor of production is labor so the problem does not get too complicated. Also, just for a sake of simplicity let’s assume there only two goods apples and oranges.

An example of simple production function for apples would be $A=L^{1/2}$ and for oranges $O=2L^{1/2}$ and let’s assume that the maximum amount of labor hours country has available is 100 to make math simpler. This would give you PPF with corners at 10A and 20O and then some curve in between them. In real life the same calculation would be performed but production function would use more factors of production and would be estimated for all industries. That would be difficult to visualize because the graph would have dimensions equal to the number of industries and anything above 3D is very hard to plot but it would work the same way.

In this calculation you take production function and resource constraint as it is. There is always possibility that a country discovers new technology that increases efficiency or new resource, but you have to define PPF at some point of time otherwise it does not have any meaning - in long run the whole universe will became just cold lifeless void because of the entropy so for most of the time universe exists the PPF of any life form will be 0. But at present or different points of time it will be non-zero.

For example a new technology in above example for apples could change in time $t+1$ the apples production function to $A=4L^{1/2}$. Now the PPF would have corners at 40A and 20O at the time $t+1$ even though before it was smaller. However, at both periods of the time people could choose to produce not at the boundary of PPF but that would not be due to the technology or resources but due to preferences or perhaps some bad policies that prevent them to do that. Culture could affect preferences but also resource constraint - if you for example really have to observe shabbat and can’t work no matter what, but again at a point of time that’s fixed and implicitly included in PPF.

PPF is by its definition constructed by already taking technology (via production function) and amount of resources available (via the resource or budget constraint) at some time into the account so it’s not like you somehow have to add that to PPF. Of course, in real life people could argue that different econometric techniques might not capture these factors properly and might dispute your statistical methodology, but that’s whole different discussion

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  • $\begingroup$ "technically estimating" What does "technically" mean in this context? "maximum amount of labor hours country has available is 100" But how do we estimate such number? Do we assume that it's how much labor hours we will have if we turn the whole country in one giant labor camp? Do we assume perfect health of our population? Do we assume zero unemployment? $\endgroup$ – user161005 Dec 25 '19 at 15:55
  • $\begingroup$ @user161005 1/2 in this context that mean in a sense that’s it is a technical or engineering problem. That means you make an assumption like for example people in country A could work max 16 hours a day (or whatever number makes sense based on human biology or psychology etc) and then count how much available labor hours a country has. You can in that calculation take into account of sick people by setting their L to zero. You could just assume sick people away if you don’t want to be precise. In real life people don’t really make PPF calculations so it’s purely hypothetical $\endgroup$ – 1muflon1 Dec 25 '19 at 16:08
  • $\begingroup$ @user161005 2/2 but if someone would like to do it then it would be just statistical exercise. Gather data on what is the max labor supply of every person (redo this for all other factors of production - survey amount of capital, land etc). Do some fancy econometrics to get some estimates of production functions. Then use analytical software like matlab or program it in python and add system of resource constraint as constraints into system of production functions and then solution to this system where every resource is fully used would give you PPF. $\endgroup$ – 1muflon1 Dec 25 '19 at 16:14
  • $\begingroup$ @user161005 adding to my previous 2 answers while I never seen people estimating PPF proper, many scholars work on estimating the potential GDP (i.e. GDP under assumption that all resources are fully employed in the economy) - although I would not really call this PPF. This is done by estimating aggregate production function and then adding the resources and resource utilization in based on statistical estimates. You can see example here: oecd-ilibrary.org/docserver/…. $\endgroup$ – 1muflon1 Dec 25 '19 at 16:30
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    $\begingroup$ @user161005 You can infer that PPF has increased if potential GDP has increased between two point of time. However, proper PPF is not being estimated as that would be very laborious task. Developed economies have thousands of industries and millions of products, so calculating proper PPF is impractical. Thats why when it comes to maximum possible production economy can produce most research looks just at potential aggregate like potential GDP or GNP or some other aggregates. You just cant really call these PPF because there is technically no "frontier" with only one aggregate $\endgroup$ – 1muflon1 Dec 25 '19 at 16:54
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Nobody really cares about PPF of the country in the real life, we use "potential GDP" instead. As for the line between things considered possible and impossible, firstly, there is no universally agreed upon procedure for finding "potential GDP". Secondly, during calculation of "potential GDP" we either use subjective input from an expert OR make a rought estimate relying on overall statistics (No need to differentiate between what is possible and what is impossible if we just extrapolate/estimate using overall statistics).

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