Consider the goods market of a closed economy in which investment I is no longer assumed as exogenously given but depends on production Y and the interest rate i : Y=C(Y?T)+I(Y,i)+GC=c0?+c1?(Y?T)I=b0?+b1?Y?b2?i? where c0?>0,0<c1?<1,b0?>0,b1?>0,b2?>0 and c1?+b1?<1 (a) Explain the economic arguments leading to investment demand being modelled as: I=I(Y,i)(+,?)?
b) Derive the IS curve for this economy, i. e., solve for equilibrium on the goods market. c) Based on the derived result for equilibrium output, calculate the (net-)tax multiplier and the government spending multiplier: ?T??Y?,?G??Y? Furthermore, calculate the partial derivatives of equilibrium output with respect to the following parameters: c0?,c1?,b0?,b1? and b2?. Give an economic explanation for each of your findings. Finally, compare your findings with similar results calculated in Exercise (4.2)(b), where - with this being the difference to the current exercises - investment demand was assumed to be exogenously given. 2
2 The results of Exercise (4.2)(b) are: ?T??Y?=1?c1??c1??,?I??Y?=?G??Y?=?c0??Y?=1?c1?1?,?c1??Y?=1?c1?YD??