Translation:The price of the kitten is thirty euros.
The purpose of the adoption fee is to cover the cost of preparing the animal for adoption and pays for things like castration, vaccinations and a veterinary exam. (You also pay a fee when you adopt a child.)
The purpose of a purchasing price is to make money for someone, and the animal is treated as a commodity.
The -n is not added for a noun after the verb "estas" or "to be" which does not take a direct object, but rather a predicate nominative which refers back to the subject. It is added after "kostas", because then the noun is the direct object. The price is 30 euros. the price = 30 euros (Both nouns are in the nominative case.) The cat does not equal 30 euros. "The cat costs 30 euros." (Now euros is in the accusative case.) If you said "I paid 30 euros." (Euros would not equal I and it is again the direct object in the accusative case and so would take the -n.)