Question

Consider an economy in which policymakers want to increase the level of output without raising inflation. Assume that the effects of policy instruments on the targets can be represented as: • Δ?=1.3Δ?+0.3Δ? • Δ?=0.15Δ?+0.1Δ? a) Are fiscal and monetary policy linearly independent instruments? b) What policy mix would achieve a rise of 2 percent in the level of output without raising inflation? c) Now assume that Δ?= 2 Δ?. Is there any policy mix that would achieve the objectives in b? Why?.

Answer 1

(a)Yes, since the change in G and change in Y are not related to each other through an equation, they are linearly independent variables.

(b) Let the change in G be G and change in M be M

We need:

2 = 1.3G + 0.3M.............(1)

0 = 0.15G + 0.1M............(2)

1*(1) - 3*(2) we get,

2 = 0.85G + 0

=> G = 2/0.85 = 2.35

=> M = -(0.15*2/0.85)/0.1 = -3.52

Thus, we get G= 2.35 and M = -3.52 (changes in G and M)

(c) Now we have,

2 = 1.3G + 0.3M.............(1)

4 = 0.15G + 0.1M............(2)

1*(1) - 3*(2) we get,

-10 = 0.85G + 0

=> G = -11.76

=> M = (4 - (0.15*(-10/0.85)))/0.1 = 57.64