老师好，
Despite the Puritan sumptuary laws prohibiting the wearing of bright or elaborate clothing, thosewitheither a liberal education or an annual income of two hundred pounds were allowed to display their material prosperity in public.
①划线处的with假如改成having，应该是错误的吧？不对是什么原因不是have本身就表示一种状况？我弄不知道不对是什么原因。
②在其他的句子中，have began这种表达也是错的，可是为何呢？为何如此的动作不可以加完成态呢？
两个问题是不是有共通的地方呢？
我一头雾水，可能描述的不太了解，还望老师多多指点。
句子来源：GMAT OG
原题如下：
（OG20新增）Despite the Puritan sumptuary laws prohibiting the wearing of bright or elaborate clothing, if you had either a liberal education or an annual income of two hundred pounds one was permitted to display their material prosperityin public.
A if you had either a liberal education or annual income of two hundred pounds one was permitted the public display of their material prosperity
B if one had either a liberal education or annual income of two hundred pounds one was permitted the public display of their material prosperity
C having either a liberal education or annual income of two hundred pounds would allow one to publicly display their material prosperity
D those with either a liberal education or an annual income of two hundred pounds were allowed to display their material prosperity in public
E those having either a liberal education or annual income of two hundred pounds were permitted their public display of material prosperity
选项A, B, C, E 均有have annual income of...，虽然income可以是可数名词，也可以是不可数名词，但在和have搭配表示一个人的收入时，income用单数形式。比如《朗文》在income的使用方法中，给出的搭配为：
have an income
We have an income of over $100,000 a year.
也就是说，ABCE四项均在have后少了不定式冠词，这是其错误之处。只有D项没错误。
have began当然是不对的，完成时态如何能是have+过去式呢？
