question of macroeconomics

1. Consider an economy with the following functions: Yr: Ct+ It+ Gt+ NX: Ct = (1617; where is = 0.5 and 17} is the longrun trend potential output I, = 51,17; Baa, r) where a,- = 0.3, r = 3 and E = 0.4 G: = (1917,: where is = 0.2 NXt = EMF} where flux = 0 a) Derive the IS curve as the GDP gap, 17}, as a function of the real interest rate, Rt, where ~ Y: Y: = . Y: b) What is the real interest rate at which current output, if}, is equal to the longrun potential output? c) According to Ricardian equivalence, what is the impact of a temporary increase in government spending ( g rises for one period)? Assume the extra spending is nanced by government borrowing. Explain what happens to consumption today and in the following periods, and why