Q. Explain about Household savings?

Remember that consumption may refer to observed consumption as well as to demand for consumption. The same is true for 'household savings', which may be observed household savings as well as the supply of savings by household sector. Supply of savings by the household sector is defined as net amount that all households together which to lend under numerous conditions.  

First note that for savings, we are always interested in net. Some individuals shall want to borrow and some shall want to lend and some shall want to do both. Household savings is the sum of all items where lending is described as positive amounts and borrowing as negative amounts. If you borrow money in bank, you are in effect decreasing the total amounts of savings. 

In the classical model supply of savings SH relies positively on the real interest rate in classical model. This follows by the fact that C relies negatively on r. When r increases, we consume less and save more. Hence household savings is denoted by S_H(r).