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| Figure 1: A Hydro-Electric Facility |
The appearance and effects of joint production are sometimes hard to see, and they often require a degree of abstraction to understand1. For example, suppose only one process exists in the Leontief input-output matrix to produce a certain pair of joint products. And no other process produces either one of them alone. It does not necessarily follow that the Leontief matrix is non-square. It could be that two processes exist for producing another product, but with different ratios of inputs. The inputs in this pair of processes consist, among others of the pair of joint products. And so prices of production still can be explained without specifying demand schedules for consumers. The net output of the economy can vary in some range of proportions with the same prices of production. Demand and supply remain asymmetrical.
But I want to concentrate in this post in describing a specific combination of processes for making a joint product. The joint products, at some level of abstraction in this case, are peak-time and off peak-time electricity2. The apparatus illustrated in the figure above produces these joint products.
The dam has an associated generator. During off-peak hours, some of the resulting electricity is used to pump water up the hill and into the storage area. Only some of the off peak-time electricity is delivered to the grid.
On the other had, during peak hours, two generators are operated, and all of the generated electricity is delivered to the grid. The underground pipe to the storage area flows backwards from how it flows during off-peak hours. This water flowing downwards is used to operate one of the generators, the one not operating during off-peak hours.
It seems to me these are not fixed coefficient processes. I imagine more off-peak hours electricity can be delivered to the grid if not as much water is pumped up to the storage area. So peak and off-peak electricity can be traded off to some extent, but not one for one. Some of the off-peak electricity would be lost to operating the pump and necessary3 inefficiencies in operating the generators. So one unit of off-peak hours electricity would be sacrificed for less than one-unit of peak hours electricity. But the configuration of the apparatus, I gather, sets a limit to maximum amount of electricity that can be generated.
So we see here an application of Sraffian economics in energy economics.
Footnotes- Bertram Schefold has written much on this theme, including on applied problems.
- Milk and gasoline are both measured in gallons. But nobody would say the ratio of the price of milk for delivery at one point of time to the price of gasoline at another point of time is an interest rate, despite what a superficial and mistaken dimensional analysis might say. Likewise, the ratio of the price of peak-time electricity to off-peak time electricity is not an interest rate.
- See the second law of thermodynamics.
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3 comments:
I'm *so* glad to see you pick up on my peak/off peak electricity example!
"Likewise, the ratio of the price of peak-time electricity to off-peak time electricity is not an interest rate."
If I get a promise to deliver 105 dollars next year in exchange for 100 dollars now, that's a 5% per year interest rate on dollars.
If I get a promise to deliver 105 tons of wheat next year in exchange for 100 tons of wheat now, that's a 5% per year interest rate on wheat.
If I get a promise to deliver 105 KWh electricity next hour in exchange for 100 KWH electricity now, that's a 5% per hour interest rate on electricity.
You are in the process of re-discovering the neoclassical theory of interest.
Of course, the promise is to deliver 98KWH electricity next hour in exchange for 100KWH electricity now, so that would be a (-2)% per hour interest rate on electricity. Or 98KWH electricity in five hours time in exchange for 100KWH electricity now, so that would be a (-0.4)% per hour interest rate on electricity.
Bruce: Yep. It's a negative real interest rate in that case. We see the same negative real interest rate on apples every Fall, because we expect apples price inflation to be higher than the nominal interest rate over the next few months.
We look for a tangency between the intertemporal PPF and the intertemporal Indifference curves. The slope where they kiss will equal 1+the rate of interest on apples (or electricity, or wheat, or whatever). It's the standard Irving Fisher diagram.
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