Answer to Question #197131 in Economics for Ala Ana

Question

An economy is described by the following equations:

𝑪 = 𝟓𝟎𝟎 + 𝟎. 𝟕𝟓(𝒀 − 𝑻) ( 𝑴 / 𝒑 ) ^𝒅 = 𝒀 − 𝟐𝟎𝟎𝒊

𝑰 = 𝟏𝟎𝟎𝟎 − 𝟓𝟎𝒊 𝑴 = 𝟔𝟎𝟎0

𝑮 = 𝟏𝟎𝟎𝟎 𝒑 = 𝟐

𝑻 = 𝟏𝟎𝟎𝟎

a) Derive and graph the IS curve and the LM curve. Calculate the equilibrium interest rate and level of income. A label that points A on the graph.

b) Suppose that the taxes are cut by 20%. Assuming that the money supply is held constant, what are the new equilibrium interest rate and level of income. What is the tax multiplier?

c) Now assume that the central bank adjusts the money supply to hold the interest rate constant. What is the new level of income? What must the new money supply be? What is the tax multiplier?

d) Now assume that the central bank adjusts the money supply to hold the level of income constant. What is the new equilibrium interest rate? What must the new money supply be? What is the tax multiplier?

e) Show the equilibria calculated in b), c) and d) on the graph you drew in a). Label the points B, C, and D

Answer 1

a) The IS equation is:

Y = 500 + 0.75(Y - 1000) + 1000 - 50i + 1000,

0.25Y = 1750 - 50i,

Y = 7000 - 200i.

The LM equation is:

Y - 200i = 600/2,

Y = 300 + 200i.

The equilibrium interest rate and level of income are:

7000 - 200i = 300 + 200i,

400i = 6700,

i = 16.75,

Y = 300 + 200*16.75 = 3650.

b) If the taxes are cut by 20%, then both the equilibrium interest rate and level of income will increase. The tax multiplier will decrease.

c) If the central bank adjusts the money supply to hold the interest rate constant, then the level of income will increase, money supply will increase, the tax multiplier will decrease.

d) If the central bank adjusts the money supply to hold the level of income constant, then the equilibrium interest rate will increase. The money supply will decrease. The tax multiplier will not change.