Government purchase

Question 1. Suppose we have the following short-run model. Resource constrain is
Yt = Ct + It + Gt + EXt − IMt
Where Yt
is economy output, Ct
is consumption. It
is investment. Gt
is government purchase. EXt
is exports. IMt
is imports. Government purchase depends on the current state of the economy. For
example, when there is an economic recession, the government will spend more money to support
the economy. To incorporate this intuition, we will use the following equations. Also, we will
incorporate the consumption multiplier effects.
Ct
Y¯
t
= a¯c + x¯cY˜
t
Gt
Y¯
t
= a¯g + x¯gY˜
t
EXt = a¯exY¯
t
IMt = a¯imY¯
t
It
Y¯
t
= a¯i − ¯b(R¯
t − r¯)
a. Derive IS curve, and draw IS curve. (x-axis: Y˜ , y-axis: R(real interest rate)) What are the
slope and the y-intercept?
b. Suppose the multiplier effects for the government purchase changed(xg increase). What is the
impact of this change?
1
c. Assume, MP(monetary policy) curve is a horizontal line. Suppose, there is a negative demand
shock on consumption. (ac decrease) What is the impact of this shock? What is the response
of the federal reserve? Use the IS-MP curve graph to explain the impact of this shock.
d. Continue with the previous question. Explain how the change in inflation (∆π) changes when
there is a negative shock on consumption. (Use Philips Curve)