Question 1: An IS/LM Model with Proportional Income Taxation Suppose the goods-market of the economy of Macronium is described by the following equations: Consumption: C = 640 + 0.75 Ya where Ya refers to disposable (post-tax/after-tax) income. Government collects two types of taxes from households: a lump-sum (constant) tax amount of 80 units, and a proportional (flat) tax of 20% of income. Therefore, total tax revenue can be described as: T = 0.20 Y + 80 Further, you are given the following equations: Investment: I= 300 - 1000r. Government Expenditure: G = 600 Also, the money-market of the economy of Macronium is described by the following equations: Money Demand: L(r.y) = 0.5Y - 750r Money Supply: M =$6600 Average Price Level : P=$4 a. Calculate the government purchase multiplier and the lump-sum tax multiplier. b. Calculate the IS curve, i.e., write the IS curve equation for Macronium. c. Calculate the LM curve, i.e., write the M curve equation for Macronium. d. Calculate the equilibrium interest rate and income level. e. Calculate consumption, investment, taxes, private saving, public saving & national saving under this equilibrium. f. Suppose that the government of Macronium raises government expenditure by 40 units (i.e., from G is now 600+40=640). Calculate the effect of this change on the equilibrium output and real interest rate. g. Suppose that Fed wants to get the economy back to the equilibrium output level you calculated in part d, and to achieve this goal, it plans to change the money supply in the right direction. How much change in nominal money supply should the Fed make (also in what direction) and what is the new real interest rate after Fed's intervention? Why do you think this happens? h. Calculate the new values of consumption, investment, taxes, private saving, public saving & national saving after the Fed's policy intervention this equilibrium. Do you observe any crowding out taking place? If so, what level of crowding out do you calculate?
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IS LM model, shows relation between goods market,
a)
Y = C
Government purchase multiplier = 1 / (1 - MPC (1-t))
MPC = 0.75
t = 0.20
Government purchase multiplier = 1 / (1 - 0.75 (1-0.20))
Government purchase multiplier = 1 / (1 - 0.75 (0.80))
Government purchase multiplier = 1 / (1 - 0.60)
Government purchase multiplier = 1 / 0.40
Government purchase multiplier = 2.5
Lump sum tax multiplier = - MPC / (1 - MPC (1-t) )
Lump sum tax multiplier = - 0.75 / (1 - 0.75 (1-0.20))
Lump sum tax multiplier = - 0.75 / (1 - 0.75 (0.80))
Lump sum tax multiplier = - 0.75 / (1 - 0.60)
Lump sum tax multiplier = - 0.75 / 0.40
Lump sum tax multiplier = - 1.875
b)
IS Curve
Y = C + I + G
Y = 640 + 0.75 (Yd) + 300 - 1000 r + 600
Y = 640 +0.75 (Y - T) + 300 - 1000 r + 600
Y = 1540 + 0.75 (Y - 0.20 Y - 80) - 1000 r
Y = 1540 + 0.75 (0.80 Y - 80) - 1000 r
Y = 1540 + 0.60 Y - 60 - 1000 r
Y = 1480 + 0.60 Y - 1000 r
Y - 0.60 Y = 1480 - 1000 r
0.40 Y = 1480 - 1000 r
Y = 1480/0.40 - 1000 r / 0.40
Y = 3700 - 2500 r
IS curve equation is Y = 3700 - 2500 r
c) LM curve
Money demand = Money supply / Price level
0.5 Y - 750r = 6600 / 4
0.5 Y - 750r = 1650
0.5 Y = 1650+ 750r
Y = 1650/0.5 + 750r/0.5
Y = 3300 + 1500r
LM curve equation is Y = 3300 + 1500r
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