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The grammatical subject is "relationship."

"According to the law of demand" is a sentence modifier and should have a comma after it.

The main verb is "exists," and its grammatical subject is "relationship." "Negative" is an adjective that modifies "relationship."

The rest of the sentence, from "between" to the end, is a prepositional phrase with two objects--"price" and "quantity"--and several modifiers. The whole prepositional phrase is adverbial and modifies "exists."

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Q: What is the subject in this sentence - According to the law of demand a negative relationship exists between the price of a good and the quantity demanded?
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Related questions

What is a negative relationship between the quantity demanded and price called?

Propensity to consume


The negative relationship between the quantity demanded of a commodity and its price can be explained by the principle of?

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What kind of relationship does the demand curve have in relation to supply?

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the law of demand. an inverse relationship between the quantity demanded and the price of the product (the lower the price the higher the quantity demanded).