1. algebra of the income-expenditure model consider a small economy that is closed to trade, so that its net exports are zero. suppose that the economy has the following consumption function, where c is consumption, y is income (real gdp), ip is planned investment, g is government purchases, and t is taxes: c = $40 billion+0.5×(y – t) suppose g=$215 billion, ip=$50 billion, and t=$10 billion. given the consumption function and the fact that, in a closed economy, planned expenditure can be calculated as y=c+ip+g, the equilibrium income level is $ billion. suppose that government purchases are reduced by $100 billion. the new equilibrium level of income will be equal to $ billion. based on the effect of the change in government purchases on equilibrium income, you can tell that this economy's multiplier is equal to