代购的英文：
buy on sb.'s behalf
act as a purchasing agent

参考例句：

Our comprehensive service company offers services including purchase, sale, storage and transportation for customers.
代购、代销、代储、代运，是本综合服务公司的眼务内容。

buy是什么意思：
n. 所购的物品；便宜货；买卖
v. 买；获得；购得；收买；相信

Buying bonds is safer than buying stocks.
买债券比买股票风险小。

It's a good buy at that price.
这是一笔价钱合算的买卖。

That shirt was a really great buy.
这个衬衫真是便宜货。

behalf是什么意思：
n. 代表；利益

They campaigned on behalf of asylum seekers.
他们为政治难民发起运动。

We work for national behalf.
我们为国家的利益工作。

I'm collecting on behalf of the blind.
我正在为盲人进行募捐。

act是什么意思：
n. 行为，行动；法案；法令；一幕，段；装腔作势
v. 行动；扮演；假装；装作；起作用，见效；举动像

This is an act of depressing.
这是使人压抑的行为。

The act of disappointing.
使人失望的行为

We must act, we must act quickly.
我们必须行动，立即行动。