why r fall , C will then rise??

For the point you brought up, there should be an assumption which states that there are only a few ways for people to manage their income:

1: Put them all in saving account
2: Investing in alternative markets
3: Spend them in the good market (personal consumption)

A decrease in interest rate would certainly reduce the incentive for people to save their money because a lower rate decreases the return of saving.

Therefore, people would prefer making some investment or spend them in the good market. The marginal increment and allocation of those money in investment sector and the consumption sector can depends. Nevertheless, the increase in consumption would be resulted due to rate decrease.