I= 150- 10i S = -50 + .25(Y - T) G = G_0 T = T_0 M^s = M^0 M^D = 40 + .10Y = 10i
ID: 1225810 • Letter: I
Question
I= 150- 10i S = -50 + .25(Y - T) G = G_0 T = T_0 M^s = M^0 M^D = 40 + .10Y = 10i A. Derive the IS cun/e for this economy (symbolically). Determine the direction of the effects of the following on the equilibrium interest rate and equilibrium level; of income (Y) you must show how you drew this conclusion): Money supply (M^s)? Government Purchases (G) Taxes (T) Let G=50, T=100 and M^s = 100. Derive the IS and LM curves from this information. What are the equilibrium interest rate and level of income? Suppose that the level of Y is 20 percent less than necessary to achieve full employment. How much do taxes need to be changed by in order to close the gap between full-employment income and current income?Explanation / Answer
(A) Equation of IS: Y = C + I + G
Y - C = I + G
S = I + G
- 50 + 0.25(Y - T) = 150 - 10i + G0
- 50 + 0.25(Y - T0) = 150 - 10i + G0
- 50 + 0.25Y - 0.25T0 = 150 - 10i + G0
0.25Y = 200 - 10i + G0 + 0.25T0
Y = 800 - 40i + (4G0 + T0) ......(1) [Equation of IS curve]
(B)
(1) LM equation is: MS = MD
M0 = 40 + 0.1Y - 10i ......(2) [Equation of LM]
As money supply increases, the money supply curve shifts right. To maintain equilibrium, right hand side of LM curve equation has to increase as well, which is possible at a higher income and lower interest rate.
So, as MS increases (decreases), Y increases (decreases) and i decreases (increases).
(2) As G increases, Y increases as seen from IS equation. Also, higher G will lead to higher borrowing, which raises interest rate (i).
So, as G increases (decreases), Y increases (decreases) and i increases (decreases).
(3) As T rises, disposable income falls and consumption demand falls, as a result of which Y falls and i falls too.
So,
As T increases (decreases), Y decreases (increases) and i decreases (increases).
(C) G = 50, T = 100, MS = 100
From IS equation,
Y = 800 - 40i + (4G0 + T0)
Y = 800 - 40i + (4 x 50 + 100)
Y = 800 - 40i + (200 + 100)
Y = 800 - 40i + 300
Y = 1,100 - 40i
From LM curve,
M0 = 40 + 0.1Y - 10i
100 = 40 + 0.1Y - 10i
0.1Y = 60 + 10i
Y = 600 + 100i
In equilibrium,
IS = LM
1,100 - 40i = 600 + 100i
140i = 500
i = 3.57
Y = 600 + (100 x 3.57) = 600 + 357 = 957
This is full-employment Y.
Actual Y = 957 x 80% = 765.6
Gap = 957 - 765.6 = 191.4
Tax multiplier = - (1 - MPS) / MPS = - 0.25** / (1 - 0.25) = - 0.25 / 0.75 = - 0.33
As T decreases by $1, Y increases by $0.33.
To increase Y by $191.4, T must decrease by $191.4 / 0.33 = $580.
**From saving function, MPS = 0.25