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Question - Help Needed

Peyton Manning

Hey guys, need some help here. Ive been given the following question:

How does monetary contraction in an open economy with flexible exchange rates affect the consumption, investment, output and net exports? What does UIP condition imply?

Ive got the investment and output parts pretty much, but how does it affect consumption, and net exports (bearing in mind the flexible exchange rates)?

Also, I was going to just abandon this question, but ill throw it down if anybody feels like being an absolute legend and giving me some answers

Consider the production function Y = K^0.5 N^0.5
a) Suppose that ô = 0.1 (depreciation rate) and s = 0.2. COmpute steady-state K/N, Y/N and C/N. Graphically illustrate the steady state.
b) Suppose ô = 0.1 but saving rate increases to s = 0.5. Solve for the steady state K/N, Y/N and C/N. Illustrate these changes graphically.
c) Suppose s = 0.2 but depreciation rate decreases to ô = 0.05. Solve for the steady state K/N, Y/N and C/N. Illustrate the changes graphically.
d) When ô = 0.1, what is the saving rate that maximises C/N?

I dont expect anyone to answer this one though

Maybe someone will astound me!

Thanks guys!

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Time Magazine

Archimedes wrote: »

How does monetary contraction in an open economy with flexible exchange rates affect the consumption, investment, output and net exports? What does UIP condition imply?

This one is textbook. It's more than likely in your lecture notes.

Consider the production function Y = K^0.5 N^0.5
a) Suppose that ô = 0.1 (depreciation rate) and s = 0.2. COmpute steady-state K/N, Y/N and C/N. Graphically illustrate the steady state.
b) Suppose ô = 0.1 but saving rate increases to s = 0.5. Solve for the steady state K/N, Y/N and C/N. Illustrate these changes graphically.
c) Suppose s = 0.2 but depreciation rate decreases to ô = 0.05. Solve for the steady state K/N, Y/N and C/N. Illustrate the changes graphically.
d) When ô = 0.1, what is the saving rate that maximises C/N?

What year are you in and what college do you go to? Are you supposed to derive the conclusions of the Solow model? If I'm on the right lines, you'll get plenty of help deriving them from these notes from some guy who I think works for NAMA.

Peyton Manning

Thanks TE, that first question was actually straightforward enough. Almost embarassed I asked about the consumption, I was thinking of something completely different! Although still having difficulty with the second question. I havent come across the Solow model before so I doubt its the method we are supposed to use. Not sure what to do next!

Time Magazine

Archimedes wrote: »

Thanks TE, that first question was actually straightforward enough. Almost embarassed I asked about the consumption, I was thinking of something completely different! Although still having difficulty with the second question. I havent come across the Solow model before so I doubt its the method we are supposed to use. Not sure what to do next!

I need to know what level you're at because there's no need deriving the main results by hand if you're only expected to know the end result. What year are you in and what is your textbook?

Peyton Manning

Im in second year, the book we are using is Macroeconomics (5th ed) by Olivier Blanchard, published by Pearson International.

Time Magazine

Archimedes wrote: »

Im in second year, the book we are using is Macroeconomics (5th ed) by Olivier Blanchard, published by Pearson International.

Okay those notes will be far too advanced for you then.

I'm not going to give you the answers, but I've no problem pointing you in the right direction.

I presume for 2nd year you'll just have to learn off the formulas that stem from the Solow model, whether you know that's what you're doing or not

. Basically the Solow model is the [latex]\displaystyle Y = A K^\alpha N^{(1-\alpha)}[/latex] Cobb-Douglas that you're dealing with, but based around long-run growth.

In the Fourth Edition, Chapter 11: Saving, Capital Accumulation, and Output is what you're looking for. I'm sure things haven't changed much from 4e to 5e, so it's probably somewhere between Chapters 10-12.

The graphs you're looking to draw will look a bit like this:

Go read that chapter and those that follow in accordance with your lecture notes (if they exist). That topic is imho the most important thing in macroeconomics for undergrads to learn.

Peyton Manning

Thanks for the help man, really appreciate it! Ill give those chapters a read as soon as I get home

Peyton Manning

Ok, this is what I came up, does it look right? I could be way off

Y = K^0.5 N^0.5.................ð = 0.1, s = 0.2

Y = K^0.5 N^0.5 = √K√N
Y/N = (√K√N)/N = (√K)/(√N) = √(K/N)
f(Kt/N) = √(Kt/N)
(Kt+1)/N - Kt/N = s√(Kt/N) - ð (Kt/N)

s√(K*/n) = ð(K*/N)
s² K*/N = ð²(K*/N)²

Now for the answers....

K*/N = (s/ð)² = (0.2/0.1)² = 4

Y*/N = √(K*/N) = √(s/ð)² = s/ð = 0.2/0.1 = 2

C/N = Y/n - ð(K/N)
C/N = s/ð - ð(s/ð)² = (s(1-s))/ð = (0.2(1-0.2))/0.1 = 1.6

The graph Ive drawn is like this....

That would be for part (a), with it pretty much the same for parts (b) and (c) with different numbers plugged in for savings and depreciation. Am I anywhere near correct?

Peyton Manning

Ok another 2 questions Im stuck on

1. The Structure of an economy is summarised by the following equations:

C = 100 + 0.7(Y-T)
I = 100 + 0.1Y - 1000i
G = 100
T = 100
(M/P)^d = 2Y - 46000i
M = 500
P = 1

where C is consumption, I is investment, Y is income, i is the interest rate, G is government spending, T is taxes, (M/P)^d is real money demand, M is nominal money supply and P is price level, and hence M/P is real money supply.

(a) When i = 0.05 or 5%, derive the deman for goods, Z, equation
(b) Using your answer in (a), plot the ZZ line
(c) Using your answer in (a), find equilibrium output (there is no money market effect here)
(d) If tax decreases to 60, how much will output change?

I have the above questions done no problem. It is with the following I am having trouble:

(e) Suppose now that interest rate is no longer %5. Derive the equation for the IS curve when T=100.
(f) Derive the equation for the LM curve.
(g) What is the equilibrium output in this general case with money markets?
(h) What is the equilibrium interest rate?
(i) What is the level of saving at equilibrium? Show it equals investment.
(j) How much will output change if T decreases to 60 in this general case.
(k) Explain why your answers in (d) and (j) differ.

Any help appreciated. A step by step solution would help me out so much, Im really running out of time to get this paper handed in (due in by 4:30 tomorrow). Again, thanks to anyone who can help me (especially The Economist who has been of huge help so far, I cant thank you enough!).