What do " that" and " at a cost" mean in the following sentence?

Question

I struggles to understand the sentence in bold in the following essay because of the usage of at a cost and following the word that.

Geothermal energy is natural heat from the interior of the Earth that is converted to heat buildings and generate electricity. The idea of harnessing Earth's internal heat is not new. As early as 1904, geothermal power was used in Italy. Today, Earth's natural internal heat is being used to generate electricity in 21 countries, including Russia, Japan, New Zealand, Iceland, Mexico, Ethiopia, the Philippines and the United States. Total worldwide production is approaching 9000 MW. Some 40 million people today receive their electricity from geothermal energy at a cost competitive with that of other energy sources. However, at the global level, geothermal energy supplies less than 0.15% of the total energy supply.

I know what "at a cost" means but I looked it up again in the Cambridge Dictionary and I found the following examples which are completely understandable.

He rescued four people at the cost of his own life.

It means you take a risk, in this case his your life, you are going to lose something but it is not clear how much it will be.

The cruise ship was built at a cost of $400 million.

This sentence simply means that the cruise cost $400 million.

Can you explain to me what the sentence imply , especially at a cost and that?

Answer 1

The word cost here simply means the price. The cost of a loaf of bread is the price of a loaf of bread, for example.

In the Original Poster's extract the word cost is being post-modified by an adjective phrase headed by the word competitive:

• competitive with that of other energy sources

Because this adjective phrase is long it cannot precede the noun cost

• a competitive cost

• a [competitive with the cost of other energy sources] cost _{(ungrammatical)}

• a cost [competitive with the cost of other energy sources]

In the example above, the word cost appears twice. In the Original Poster's example, the second occurrence of the cost has been replaced with the pronoun that:

• a cost competitive with that [= the cost] of other energy sources.

Some grammarians would regard this adjective phrase as a reduced relative clause where the pronoun and the verb BE have been elided through whiz-deletion:

• a cost which is competitive with that of other energy sources.

Answer 2

1) He rescued four people at the cost of his own life.= He died saving them.

2) geothermal energy at a cost competitive with that of other energy sources. =

The cost of geothermal energy is about the same as the cost of other energy sources.

3) "that" replaces "the cost" to avoid repetition. Here are more examples:

The population of Canada is smaller than that of the US. ("that" replaces "the population")

Grammar:

(that of : singular noun)

The climate of Mumbai is better than that of Chennai.

(those of: plural noun)

The students of our school are better than those of their school.

http://www.englishgrammar.org/correct-demonstrative-pronouns/