Posts Satisfaction Unit Parity

Satisfaction Unit Parity

Purchasing power parity

While I was thinking about the pharaoh and the millionaire, a major issue that troubled me, was to fundamentally understand a way to measure and compare wealth across time or between vastly different civilizations. The most common method to do such comparisons, is using the traditional purchasing power parity but as I was exploring it with various thought experiments, I started to realize that this method has some serious limitations. I tried thus, to think of possible alternatives and what arose from this process, is the satisfaction unit parity.

Before digging into it, let’s first understand what purchasing power parity means. Let’s clarify first the purchasing power part. We essentially assume that wealth is represented by the amount of goods and services a society can buy. This is it’s purchasing power, and indeed it is the most fundamental measure of society’s wealth. The more and better goods and services a society can access (houses, food, medicines, transportation means etc.) the weallthier it actually is.

Imagine for example that we want to compare two different wealth states, the wealth of classical Athens with that of modern day Athens using the traditional purchasing power parity. We can not compare the two wealth states simply by measuring the amounts of all available goods and services, because it is impossible to know these exact amounts in each wealth state. We don’t know how much olive oil could be produced in classical Athens and use this amount to make the comparison. Moreover we have to compare using a basket of goods that contains as many goods and services as possible, in order to get an objective comparison. But if we can’t measure the absolute quantities of goods then how do we compare? The answer is that we measure the amounts of goods and services using a proxy. This proxy is the currency, or more specifically, the price of each good, which is usually easier to find.

For example, assume for simplicity that we compare the two wealth states using a basket of just one good, the olive oil. Let’s say that one litter of olive oil in classical Athens has a price of 5 drachmas while in modern day Athens it has 20 euros. This would mean that 5 drachmas have the same purchasing power with 20 euros, or 1 drachma is in parity with 5 euros. This is the purchasing power parity between drachmas and euros if we measure it using this specific basket. But how is this useful in comparing the two wealth states? Well, if we also know the monetary base of each state, in other words, if we know how many euros and how many drachmans are in existence in the two states, we could reach to a meaningful conclusion. Let’s say that there are 1 billion drachmas and 200 billion euros in existence. Since their purchasing power parity is 1 to 5 we can say that 1 billion drachmas are equivalent to 5 billion euros and that the modern day Athens is thus 40 times wealthier from the classical one. Notice though that it is 40 times wealthier in olive oil terms! This only means that a modern day athenian can access 40 times more olive oil than his classical counterpart, assuming the population is the same. In order to get the real wealth difference, we would have to create a basket of all goods and services in existance in the two states and repeat the calculations based on that basket. But here is where the problems begin.

When we compare very different wealth states, we should take into account the fact that the importance of some goods is very different between the two states. A horse for example was very useful to the ancient world. It was used by many people, it had a large trading volume and consequently it could be used as an indicator for the wealth of an ancient society. If you wanted to compare ancient Athens with ancient Rome, then the horse would definetely be part of the purchasing power basket. Today though, the horse is not that important and this means that its price is not indicative of the modern wealth state. Its current price might be high but this is because it is considered a luxury good. There are not many horses available because they are not needed that much. If we had included it in the modern day basket then it would have a skewing influence to the result, which must be counter balanced by other goods with the opposite behaviour.

The needs that the horse used to cover, are satisfied today by alternative goods, for example the automobile. Which brings us to another problem. There are many important goods like the car, that exist in one state but not in the other. What we should do in these cases? A possible solution would be to use two baskets of goods, one for each wealth state and apart form the common goods, fill them with different goods that satisfy the same need. For example the ancient athenian basket would contain the horse but the modern day basket the car. This method though has a very important limitation. It doesn’t take into account the quality difference between the goods. We should agree that a car satisfies the transportation need better than a horse. It is a major upgrade which is an achievement of a wealthier society and we should find a way to take this into account.

Satisfaction unit parity

This brings us to the satisfaction unit. The main idea is that instead of comparing the price of goods, we compare the price of satisfying the underlying fundamental need at the same degree. Instead of using a basket of goods, we use a basket of needs. We create a scale between 0 and 100 for every need, where 100 means that this need is satisfied at the maximum degree, and 0 that it is not satisfied at all. Then we use that scale to grade any good that satisfies this need.

In our simplistic example, instead of creating two baskets and comparing the price of a horse with that of a car, we create one common basket that contains the transportation need. Theoretically the best way to satisfy this need would be to have the power to be instantly transported anywhere you want, something like teleportation. That would get a score of 100 units. The horse and the car would lie somewhere within that scale, with a score between 0 and 100. Giving a score to each one of them is definetely a challenge that requires certain assumptions, but for the sake of understanding the main idea, let’s overcome these challenges by making some rough estimates. Let’s assume that the scale is linear, and that a car is 10 times better than a horse in satisfying the transportation need. Let’s also assume that we give the horse a score of 2 units which would give the car a score of 20 units. How does these scores, which represent the quality difference between the two goods, affect the comparison between the two wealth states?

Assume that a horse in classical Athens costs 500 drachmas while a modern day car 10000 euros. Without taking into account the quality of goods, we would calculate a parity of 1 drachma to 20 euros. Assuming the monetary bases are 1 billion drachmas and 200 billion euros respectively, we can calculate that 1 billion drachmas is equal to 20 billion euros which means that modern day Athens with its 200 billion euros, is 10 times wealthier.

If we take into account the quality of goods though, then we get a different result which is much closer to reality. The horse with a price of 500 drachmas, satisfies the transportation need with a score of 2. This means that 1 unit of satisfaction costs 250 drachmas. On the other hand, the car with a price of 10000 euros, satisfies the transportaion need with a score of 20 which means that 1 unit of satisfaction costs 500 euros. We can understand, that using this method we have something common to compare. The unit of satisfaction. We can satisfy our need for transportation at the same degree, by spending 250 drachmas or 500 euros respectively. This means that the satisfaction unit parity is 1 drachma to 2 euros while the previously calculated traditional purchasing power parity was 1 drachma to 20 euros. This would make the drachma 10 times weaker in comparison and would give a modern Athens which is 100 times wealthier from the classical Athems instead of just 10.

The satisfaction unit parity method might be useful for comparing wealth states with large differences with each other, where the number of common goods is small, and the quality difference between the goods is meaningfully large. It seems ideal for comparing societies with a large distance in the evolution scale. I would argue though that given the exponential evolution rate of our modern era, it might make sense to have comparisons of modern wealth states that are 20 or even 15 years apart.

Of course trying to compare using this method is not easy. The satisfaction unit parity requires the construction of a basket of needs and more importantly, the grading of goods and services within a satisfaction scale. Finding a grading process that can objectively measure the degree to which every good or service satisfies a specific need and place it accordingly in the scale, is quite a challenge.