Question

A = C + I + G + X - M C = 500 + 0.5Y – 200i I = 14000 + 0.2Y– 200i G = 1200 - 0.1Y X = 2000 M= 1000 -.05Y Y = A L = 0.33Y – 25i (M/P) = 3000 L = (M/P)

e. If the government increases spending G by 100:

i. What would the new IS Curve look like?

ii. What would the new LM curve look like?

iii. What would the new equilibrium income Y and Interest I be?

iv. At this new equilibrium, what would the level of Investment spending be?

Answer 1

Solution:

i) Finding the IS curve:

IS curve is obtained through equilibrium in the goods market, by equating real income/output, Y and aggregate expenditure, A

So, with A = C + I + G + X - M

A = (500 + 0.5Y - 200i) + (14000 + 0.2Y - 200i) + (1200 - 0.1Y) + (2000) - (1000 - 0.05Y)

A = 16700 + 0.65Y - 400i

So, at equilibrium, Y = A

Y = 16700 + 0.65Y - 400i

0.35Y = 16700 - 400i

This was the required IS curve. Now, if government spending, G, increases by 100, new IS curve would be:

0.35Y = (16700 + 100) - 400i

0.35Y = 16800 - 400i

ii) Note that government spending affects only the goods market, and not the money market. So, LM curve will remain unchanged. Deriving the new (same as old) LM curve:

Equating the money demand, L, with real money supply, (M/P)

L = (M/P)

0.33Y - 25i = 3000

0.33Y = 3000 + 25i

This is the required LM curve

iii) Finding the equilibrium values of Y and i:

Equilibrium occurs where the goods and money market, both clear. Thus, both IS and LM curves must satisfy simultaneously.

0.35Y = 16800 - 400i

0.33Y = 3000 + 25i

Solving the two equations we get:

(16800 - 400i)/0.35 = (3000 + 25i)/0.33

5544 - 132i = 1050 + 8.75i

(132 + 8.75)i = 5544 - 1050

i = 4494/140.75 = 31.93

So, Y = (16800 - 400*31.93)/0.35 = 4028/0.35 = 11508.57

So, equilibrium level of interest rate is 31.93% and equilibrium level of income is $11,508.57

iv) At the new equilibrium level, investment spending, I = 14000 + 0.2Y - 200i

I = 14000 + 0.2*11508.57 - 200*31.93

I = 14000 + 2301.714 - 6386

I = $9,915.714