闪电代写 -代写CS作业_CS代写_Finance代写_Economic代写_Statistics代写_代码代做_IT代写_加急帮助

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

ECON5002

Tutorial 4 (The IS-LM Model)

1. Consider ﬁrst the goods–market model with constant investment: C = c0 + c1 (Y–T), and I¯, G and T are given

(a) Solve for equilibrium output. What is the value of the multiplier?

Now, let investment depend on both sales and the interest rate:

I = b0 + b1Y– b2i

(b) Solve for equilibrium output. At a given interest rate, is the eﬀect of a change in

autonomous spending bigger than what it was in (a)? Why? (Assume c1 + b1 < 1.)

M/P = d1Y– d2i

Assume the central bank ﬁxes the money supply.

(c) Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM relations.) Derive the multiplier (the eﬀect of a change of 1 in autonomous spending on output).

(d) Is the multiplier you obtained smaller or larger than the multiplier you derived in your answer to (a)? Please explain how your answer depends on the parameters in the be- havioural equations for consumption, investment and money demand.

Instead, now assume the central bank sets the rate at i0 .

(e) Solve for the equilibrium level of the money supply that the central bank will have to achieve with open-market operations.

2. Consider the following IS–LM model:

C = c0 + c1 (Y–T)

I = b0 + b1Y– b2i

M/P = d1Y– d2i

Assume the central bank keeps the money supply constant.

(a) Solve for equilibrium output.

(b) Solve for the equilibrium interest rate.

(d) Under what conditions on the parameters of the model (for example, c0, c1, and so on) will investment increase when G decreases? (Hint: If G decreases by 1 unit, by how much does I increase?)

Now assume the central bank keeps the interest rate constant at i = i0 .

(e) If the central bank chose to lower the interest rate so that the money supply was the same as before the ﬁscal consolidation, what would be the eﬀect of the ﬁscal policy on investment?

3. Consider the following IS–LM model with the central bank controlling the interest rate:

C = 200 + .25YD

I = 150 + .25Y– 1000i

G = 250

T = 200

(M/P)d = 2Y–8000i

i = i0 = 0.05

(a) Derive the IS relation. (Hint: You want an equation with Y on the left side, all else on the right.)

(b) Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation with i on the left side, all else on the right.)

(c) Solve for equilibrium real output. (Hint: Substitute the value for the interest rate into the IS equation and solve for output.)

(d) Solve for the equilibrium real money supply. (Hint: Substitute the value you obtained for Y in (c) into the IS equation and solve for M/P.)

(e) Solve for the equilibrium values of C and I and verify the value you obtained for Y by adding up C , I and G.

(f) Now suppose that the interest rate, i0 was cut to 3 per cent (that is, 0.03). Solve for Y , M/P , C and I, and describe in words the eﬀects of an expansionary monetary policy.

(g) Set the interest rate back to 5 per cent. Now suppose that government spending increases to G = 400. If the central bank keeps the interest rate unchanged, ﬁnd the eﬀects of this ﬁscal expansion on Y and C . If the central bank responds by raising the interest rate by enough so that M/P is the same value as you found in part (d), what would be the eﬀect on Y , i and C? Summarise the eﬀects of an expansionary ﬁscal policy on Y , i and C .