The confusing concept of shadow prices
Discussions on simultaneous markets are underway. The idea is to integrate the supply and demand adjustment market and the wholesale electricity market, which makes the discussion complicated.
There are many difficult concepts, but one of them is shadow prices. What is a shadow price in a simultaneous market? I will explain it briefly.
Shadow price is marginal cost
First, to get to the conclusion, shadow price is marginal cost. Shadow price is the increase in cost on the supply side when demand increases marginally by one unit from a state where supply and demand are in equilibrium in a simultaneous market.
Why do we use the complex expression “shadow price”? How is it different from the “marginal cost” traded in the wholesale market? I will explain this point.
The important thing is that “the highest variable cost is not necessarily the marginal cost.”
I will explain it numerically using the minimum output constraint as an example.
1. General marginal cost
Demand Energy 300
Power source 1 Energy 160 Marginal cost 11 yen
Power source 2 Energy 140 Marginal cost 12 yen
This is a general state. If the demand increases marginally by 1 unit in this state, the supply of power source 2 will increase, so the marginal cost will be 12 yen.
2. Minimum output constraint
Demand Energy 320
Power source 1 Energy 160 Marginal cost 11 yen
Power source 2 Energy 145 Marginal cost 12 yen
Power source 3 Energy 15 Marginal cost 14 yen
*Minimum output of power source 3 is 15 (maximum output of power source 2 is 150)
Let’s say that the increased output of power source 2 is not enough to meet the increased demand of 20, so power source 3 is started. The minimum output of power source 3 is 15. Therefore, power source 3 has no choice but to generate 15 electricity. On the other hand, power source 2 has a surplus of 5.
What happens if the demand increases marginally by one unit in this state?
Yes, the supply of power source 2 increases, and the marginal cost becomes 12 yen.
The highest variable cost is 14 yen for power source 3, but power source 3 generates 15 units of electricity due to its minimum output constraint. In this state, it is actually power source 2 that meets the marginal demand, so 12 yen becomes the marginal cost.
By the way, at this time, the wholesale price in the wholesale electricity market is 14 yen (the marginal cost of power source 3) due to a single price auction.
*For simplicity, the terms output and amount of electricity are not strictly distinguished.
It is expressed as a “shadow price” because it is hidden.
When considering power source constraints in this way, the cost hidden in the highest marginal cost may be the true marginal cost. In the above example, the true marginal cost (12 yen) appears to be “hidden” in the highest marginal cost (14 yen), so it is expressed as a shadow price.
Shadow price is a very simple concept like this. There are many expressions in the current electricity market discussion that are difficult to understand. This is due to the use of overseas expressions as is, and bureaucrats using invented words.
Going forward, this site will continue to provide explanations with an emphasis on clarity.