Question

Consider a closed economy as represented by the following equations:

C = 100 + .5YD
I = 200 + .1Y – 800i T = 200
G = 200
YD = Y - T

(1) Derive the IS equation from the equilibrium position of goods market. Draw the IS curve on the graph. (10 points)In the money market, assume the real money demand is (M d/P) = Y – 1,000i; and the real money supply is (Ms/P) = 700.
(2) Derive the LM relation and draw the LM curve on the graph in part (1).

(3) Solve for the equilibrium output Y and equilibrium interest rate i when both goods market and money market are at the equilibrium. Identify this equilibrium point on the graph you draw in part (1).

(4) Suppose now the tax decreases from 200 to 100. As a result of this tax cut, how much is the new equilibrium output Y? Calculate the multiplier of tax cut.

(5) Suppose now the tax remains at 200, but the government spending G increases from 200 to 300. Calculate the government spending multiplier.

Answer 1

(1)

Goods market equilibrium occurs at the following point:

Y = C +I+G

=> Y = 100 + 0.5YD + 200 + 0.1Y -800i + 200

=> Y = 500 + 0.5(Y-T) + 0.1Y - 800i

=> Y = 500 +0.5(Y -200) + 0.1Y - 800i

=> Y = 500 + 0.5Y - 100 + 0.1Y - 800i

=> Y - 0.5Y - 0.1Y = 400 - 800i

=> 0.4Y =400 - 800i

=> Y = (400 - 800i)/0.4

=> Y = 1000 - 2000i

IS equation: Y = 1000 - 2000i

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(2) (M d/P) = Y – 1,000i; and the real money supply is (Ms/P) = 700.

At money market equilibrium point; (Md/P) = (Ms/P)

=> Y - 1000i = 700

=> Y = 700 + 1000i

LM equation: Y = 700 + 1000i

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(3) IS equation: Y = 1000 - 2000i

LM equation: Y = 700 + 1000i

At equilibrium point; IS = LM

=> 1000 - 2000i = 700 + 1000i

=> 1000 - 700 = 1000i + 2000i

=> 300 = 3000i

=> i = (300 / 3000)

=> i = 0.1

Equilibrium interest rate is 0.1

and

Y = 700 + 1000i

=> Y = 700 + 1000(0.1)

=> Y = 700 + 100

=> Y = 800

Equilibrium output is 800

Graphically it occurs at the intersection point of IS and LM curve.

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(4) C = 100 + 0.5YD

MPC = ΔC / ΔYD

=> MPC = 0.5

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Tax multiplier = -MPC / (1-MPC)

=> Tax multiplier = -0.5 / (1-0.5)

=> Tax multiplier = -1

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Tax decreases from 200 to 100

=> ΔT = 100 - 200

=> ΔT = -100

--

Tax multiplier = ΔY / ΔT

=> -1 = ΔY / -100

=> ΔY = -1 * (-100)

=> ΔY = 100

The equilibrium Y will increase by 100

new equilibrium output = 800 + 100 = 900

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(4)

Suppose now the tax remains at 200, but the government spending G increases from 200 to 300.

=> ΔG = 300 -200 = 100

Government spending multiplier = 1 / (1-MPC)

=> Government spending multiplier =1 / (1-0.5)

=> Government spending multiplier = 1/ 0.5

=> Government spending multiplier = 2

-

Government spending multiplier = ΔY / ΔG

=> 2 = ΔY / 100

=> ΔY = 100 *2

=> ΔY = 200

the equilibrium output increases by 200

New equilibrium output = 800 + 200 = 1000

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