Re question 39 from the Level 1 Mock Exam: morning session, if someone could please explain how Y = 2,500 + 0.80 × (Y +250 – 0.30 × Y) + 500 + 0.30 × Y – 25 × r + 1,000 breaks down to;
Y = 4,200 + 0.86 × Y – 25 × r.
Y = 30,000 – 178.6 × r. It would be much appreciated 
as I’m just not getting this one. Full questions and answer below; 39. In a simple economy with no foreign sector, the following equations apply: Consumption function C = 2,500 + 0.80 × (Y – T) Investment function I = 500 + 0.30 × Y – 25 × r Government spending G = 1,000 Tax function T = –250 + 0.30 × Y Y: Aggregate income r: Real interest rate If the real interest rate is 3% and government spending increases to 2,000, the increase in aggregate income will be closest to: A. 1,000. B. 1,163. C. 7,143. Answer = C “Aggregate Output, Prices, and Economic Growth,” Paul R. Kutasovic and Richard G. Fritz 2012 Modular Level I, Vol. 2, pp. 232–240 Study Session 5-17-f Explain the IS and LM curves and how they combine to generate the aggregate demand curve. C is correct. With no foreign sector, the GDP identity is Y = C + I + G. With substitution from the equations above, Y = 2,500 + 0.80 × (Y – T) + 500 + 0.30 × Y – 25 × r + 1,000 = 2,500 + 0.80 × (Y +250 – 0.30 × Y) + 500 + 0.30 × Y – 25 × r + 1,000. Y = 4,200 + 0.86 × Y – 25 × r. Y = 30,000 – 178.6 × r. At 3%, Y = 30,000 – 178.6 × 3 = 29,464. Alternatively, Y – 0.86Y = 4,200 – 25 × r 0.14Y = 4,200 – 256 × r.