The second strategy that can be used by power generation firms to affect prices involves submitting manipulative offers to the RTO market operator in order to artificially increase prices. This is sometimes called "economic withholding" because while the plant isn't physically taken out of the market, its owner winds up pricing it out of the market.

Economic withholding tends to be a good strategy when transmission constraints are binding, limiting the amount of local competition for a specific power plant. As an example, we'll use the two-node network in the figure below. The marginal cost of Generator 1 is $20/MWh and the marginal cost of Generator 2 is $40/MWh. Again, we'll ignore the fixed costs here. The demand curve is given by P = 200 - 2(G1 + G2). There is also a 50 MW limit on the transmission line.

Let's first take a look at what would happen if this electricity market behaved competitively. Suppose that both power generators submit supply offers to the RTO equal to marginal costs. You should check yourself to see that the market-clearing level of demand is 80 MWh. Generator 1 will produce 50 MWh (because that's how much the transmission line can carry, and all the demand is located at Node 2), while Generator 2 produces 30 MWh. The LMP at Node 1 is $20/MWh, while the LMP at Node 2 is $40/MWh.

In reality, Generator 2 would never submit a competitive supply offer. Why not? Generator 2 knows that if demand at Node 2 is 80 MWh, then the RTO must call upon Generator 2 to produce electricity, or there will be unserved demand at Node 2. In other words, Generator 2 realizes that since only 50 MW can be transferred across the transmission line, then it has a monopoly on serving any level of demand higher than 50 MWh. This monopoly power results specifically from the low capacity of the transmission line. If the capacity of the transmission line were to be increased, this would erode some of the market power possessed by Generator 2.

Let's proceed by assuming that Generator 1 submits a competitive supply offer of $20/MWh. So we know that up to 50 MWh will be provided at a price of $20/MWh. Any remaining demand will be served by a monopolist at Node 2. You may remember from your economics courses that a monopolist will set the level of output at the point where marginal revenue equals marginal cost.

What we will do is define a "residual demand curve" that captures the demand for electricity at Node 2 above and beyond what is supplied by Generator 1. The residual demand curve is:

The monopolist at Node 2 wants to maximize its profits, given that it faces this residual demand curve. Since profits are equal to revenue times quantity, we can write:

Taking the first order condition for the maximum of a function, we have:

When we plug G2 = 15 back into the residual demand curve, we get P = 100 - 2×15 = $70.

Thus, the equilibrium in this market is that G1 = 50 MWh, the LMP at Node 1 is $20/MWh, G2 = 15 MWh, the LMP at Node 2 is $70/MWh, and total consumption is 65 MWh. This is the typical monopolist result that prices are higher and quantities are lower relative to the competitive market outcome.

One common way of measuring the exercise of market power is through a metric called the Lerner Index, which calculates the proportional difference between price and marginal cost:

$$\text{LearnerIndex=(P-MC)/P}$$

A Lerner Index of zero indicates that P = MC and the market is competitive. A Lerner Index greater than zero implies some exercise of market power. The Lerner Index is also called the price-cost markup since it measures the deviation in price from the competitive level.

In our previous example, the Lerner Index for Generator 1 would be ($20 - $20)/$20 = 0. This is exactly what we should get since we assumed that Generator 1 priced competitively. The Lerner Index for Generator 2 would be ($70 - $40)/$70 = 0.43.

Here is another example that you can try yourself. Suppose that the marginal cost of Generator 1 was $10/MWh and the marginal cost of Generator 2 was $30/MWh. The transmission line connecting Nodes 1 and 2 has a capacity of 10 MWh. Demand at Node 2 is given by P = 100 - 5(G1+G2). Show that the LMP at Node 1 will be $10/MWh and the LMP at Node 2 will be $40/MWh.