## Wednesday, October 7, 2009

### The Value Problem

Economists believe they have solved the old Water-Diamond Paradox by showing how prices are determined at the margins. But how then do we value a large stock of resources when we only know the value of a marginal unit?

Consider this problem. A river catchment has 1,200 megalitres of tradeable water rights. The last trade occurred at a price of \$2,000/megalitre. Essentially this means that the last megalitre (the marginal unit), out of the 1,200 megalitre stock of water in the catchment, is worth about \$2,000. But are all the other 1,199 megalitres therefore worth \$2,000 a pop? Quite simply no. If the government compulsorily acquired half of the water in the catchment, the 600th megalitre would be worth more than the 1200th megalitre – an example of declining marginal value.

We can see how the marginal value declines by looking at the water use going on in the catchment. Small amounts are used for domestic consumption, some for watering house gardens, some for watering stock, some for watering pasture for stock, some for irrigating land with good soils, some for irrigating land with poorer soils. If less water was available, we would cease using it for low value activities, but keep using it for higher value ones. The value of the first megalitre of water is extremely high, as it would be likely devoted to human consumption.
So, using the numbers from the graph, if the quantity of water resumed was 600 megalitres, the value of the new marginal megalitre, the 600th, would be \$4,000/ML.

If we wanted to value the total stock of water before the resumption using unsound logic, we could have simply multiplied the marginal value by the quantity and found the water to be worth \$2.4million. We could then do the same after the resumption, and find that 500megalitres was also worth \$2.4million! Hang on. 600 megalitres of the resource cannot be worth exactly the same as 1200 megalitres of it unless the second 600megalitres was worthless, which it wasn’t, because the 1,200th megalitre used to be worth \$2,000.

I know, it’s ridiculous, but that’s actually how the ABS treats the value of our residential dwelling stock.

But what is really absurd is that when you actually want to sell a large chunk of the resource, the total value declines! Rather than reveal these higher value uses, thus supply shock decreases the marginal value.

This apparent paradox is easily resolved. When a large chunk of the stock of resource is put up for sale, it is a sign that the demand for that resource has declined, by exactly the amount that is put up for sale. The seller no longer demands the resource, so the sum total of demand decreases.

The graph above shows what happens when 200megalitres are put up for sale. 200megalitres of the demand curve are removed, and the new demand curve shifts to the left. The value of the 1200th megalitre drops to \$1,000. Using our flawed summation method, the resource is now worth only \$1.2million.

It appears that economic theories of value, much like the theories of Newtonian physics, break down at the extremes. This is especially the case since the value of one good, like water or housing, is dependent on the value of other complementary goods, such as crops, labour, machinery, and energy.

We can leave this conversation with some interesting questions.

Imagine Australians decided to move to a newly discovered planet. We can sell all the land and capital to the highest bidder. What would the value of the land and capital be worth without the labour force?

And, is there a value to the total physical resources on Earth? If there is, does that value depend on the population and technology available at the time – does the Earth become more valuable with more people and more production? (strangely enough there's plenty of reading on this topic here, here and here)

#### 1 comment:

1. OF course there's a total value for all the world's physical resources - it's the amount of money that would be needed to buy it.

This reflects the monetarist view that the total value of production is at all times equal to the money supply, given that goods are exchanged for money.

MV = PY, it's as simple as that. Especially if you're Alan Greenspan.