The government in the cross model

In this model when national income increases, amount individuals pay in income taxes will increase. This is since income tax is specified as a percentage of total income. Other taxes may also increase when Y increases. Though government transfers to households will decrease. Thus net taxes NT will increase when Y increases. 

Albeit NT depends on Y, is still under the control of government. NT may change even if Y doesn't change. This means that NT is part exogenous (as it may be controlled by the government) and part endogenous (as it would automatically change when Y changes). Thus we write NT(Y) but we should remember the exogenous nature of net taxes. Government savings, which is also part exogenous and partendogenous, depends positively on Y and we write: 

S_G(Y) = NT(Y) - G