Analyse the effects of the following events in the loanable fund market diagram where we have (real) interest rate (r) on the vertical axis and the quantity of loanable fund (Q) on the horizontal axis. Please ensure to explain what happens to private saving, private investment spending, and (real) interest rate, and demonstrate it changing a figure below.

a) An increase in government purchases

b) Australian business becomes very optimistic about the future course of the economy and this increases the prospect of their profitability at any given (real) interest rate. Assume the government budget balance is zero.

c) A decrease in the income tax rate.