英语翻译：现在新的价格要比我们报价时当地供应商提供的价格要高出很多。

不是啊，是新的客人指定的供应商的价格要比我们报价时当地供应商提供的价格要高出很多。

The current new price is much higher than the quotation suppliers offered to us when we quoted to you.

楼主的意思是不是想说,现在的原材料价格比当初我们报价给你时到得多(所以没有空间降价了),如果是这样的话,我建议这么写:

The raw material price is going up much than we quoted to you. Even so, we decide to keep the same price to support you. It is really no space now. Please understand and accept our quotation with many thanks.

哦,这样,那我会这么翻译:

The price from your specified supplier is much higher,comapried with the price offered by our local supplier when we quoted to you.
希望对你能有帮助.

Now the new price than we offer to local suppliers when the price should be much higher.

不是的，驻xx的办事处一般叫liaison office。 所以，就是xxxliaison office of yyy( xxx 是办事处所在的地名，城市名，等等，总之是能区别于其他办事处的名称的英文，可以是拼音，也可以是公认的英文名称，比如beijing 或者 peking，qingdao或者tsingdao，等等。 yyy是美国供应商的公司名称，如果你真的就想说美国供应商这个意思那就是 american supplier，或者 american vendor。

The new price of XX from your specified supplier is much higher than that of the local supplier when we privided our quote. XX - raw material or parts.