Answer to Question #171529 in Macroeconomics for Deandra Kay

Question

Consider the country of Morales with the following closed economy conditions:

 

Y = C + I + G     where:

 

C = 100 + 0.75Y

I = 180 – 15i

G = 100

T = 80

M^d = 0.2Y – 5i

M^s = 85

1. Determine the IS and LM relations 
2. Find out the equilibrium income Y and Interest Rate i 
3. Suppose the government increases its purchase by 60 (ΔG = 60). (4 points – show all mathematical work). You will need to redo all the process with the new purchase value which the government has done
4. Economic analysis: Make a comparative analysis of both national outputs and interest rates – no words limit 

Answer 1

1. (a)IS relation.

$Y=C+I+G$

$Y= 100+0.75Y+180-15i+100$

$0.75Y=100+180+100-15i$

$Y=506.67-20i$ : Which is IS relations.

(b) LM relation.

$\left (M^{\smash {d}}\right)=\left (M^{\smash {s}}\right)$

$0.25Y-5i = 85$

$5i=85-0.25Y$

$i=17-0.05Y$: Which is the LM relation.

2.

IS: $Y=506.67-20i$

LM: $i=17-0.05Y$

We first subtitute i in IS to get the value of Y.

$Y=506.67-20 (17-0.05Y)$

$Y=506.67-340$

$Y=166.67$

We now subtitute Y in LM to get the value of i.

$i=17-0.05Y$

$i=17-0.05 (166.67)$

$i=8.67$

(3.) Initially, G was 250. With increase of 60, the new G is 310.

New Y$=100+0.75Y+180-15i+160$

$Y=586.67-20i$

$Y=246.67$

The new income rate will be:

$i=17-0.05 (246.67)$

$i=4.67$

(4). The new equilibrium gives us lower interest rate of 4.67 compared to the initial 8.67%.