The HTM consumer is only constrained on borrowing, not on lendig.
It's consumption function will be C1=(1+p)/(2+p)[omega] in case the interesr rate is high enough for him to prefer to be a saver. IN that case he behaves as a ricardian.
When the interest rate fals to a level that he prefers to become a borrower, he can't, and hence C1=Q1-T1. In that case, a tax increase will imply a fall in C1 on a one to one basis.
A tax cut may imply an increase in consumtion on a 1:1 basis as long as he is still contrained on borrowing. But if the tax cut causes the disposable income today to rise to a level that he prefers to be a lender, then he will act as a ricardian consumer and will expand consumtion only partially.
Basically, it's consumtion function has two brackets (see exercises)
I hope this helps, otherwise let us know
It's consumption function will be C1=(1+p)/(2+p)[omega] in case the interesr rate is high enough for him to prefer to be a saver. IN that case he behaves as a ricardian.
When the interest rate fals to a level that he prefers to become a borrower, he can't, and hence C1=Q1-T1. In that case, a tax increase will imply a fall in C1 on a one to one basis.
A tax cut may imply an increase in consumtion on a 1:1 basis as long as he is still contrained on borrowing. But if the tax cut causes the disposable income today to rise to a level that he prefers to be a lender, then he will act as a ricardian consumer and will expand consumtion only partially.
Basically, it's consumtion function has two brackets (see exercises)
I hope this helps, otherwise let us know