to buy / bribe
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to buy
To obtain something, often something immaterial such as freedom, success, or peace and quiet, through great effort, sacrifice, or a high price.
Den Frieden mussten sie sich mit schmerzhaften Kompromissen erkaufen.
They had to buy peace with painful compromises.
'Erkaufen' (to buy / bribe) is an inseparable verb. The prefix 'er-' emphasizes that something is successfully obtained through the act of buying, though often at a high price that is not only financial.
Er hat sich seinen Erfolg teuer erkauft.
He bought his success at a high price.
You can distinguish the two meanings by the object. If you 'erkauft' (buy/bribe) a person, you bribe them. If you 'sich etwas erkauft' (buy something for oneself), you obtain an abstract good through sacrifice.
Der Politiker versuchte, die Journalisten zu erkaufen.
The politician tried to bribe the journalists.
In this meaning, the verb is almost always used reflexively: 'sich (dative) etwas (accusative) erkaufen' (to buy something for oneself). The dative pronoun shows for whom the benefit is obtained.
Ich musste mir die Ruhe mit einem Umzug aufs Land erkaufen.
I had to buy myself peace and quiet by moving to the countryside.
The 'price' or sacrifice one pays for what is achieved is often expressed with the preposition 'mit' (with) and the dative.
Das Unternehmen erkaufte sich den Marktvorteil mit einem hohen Risiko.
The company bought itself the market advantage with a high risk.
to attain
'erlangen' and 'erkaufen' can both mean that you achieve something, often something abstract such as freedom, success, or recognition. 'erlangen' mainly emphasizes the result after effort or time and sounds rather elevated. 'erkaufen' places more emphasis on the price paid for it: you get something only through sacrifice, great effort, or a disadvantage. If you want to say neutrally that someone achieves something, 'erlangen' fits better. If the high price is important, 'sich etwas erkaufen' is more precise.
Der Verein erkaufte sich den Sieg mit einem sehr hohen Verletzungsrisiko.
The club bought the victory at the cost of a very high risk of injury.
Durch jahrelanges Üben erlangte sie große Sicherheit beim Sprechen.
Through years of practice, she gained great confidence when speaking.