Any Economists out there?

[death666bl00ms]

I could use some help....

 

 

 

I am currently in Econ 305 (Intermediate Macroeconomics), and I am having some trouble with this homework. Before I get started, I want to say that I do NOT want the answer. Merely, I want to know if I am on the right track, and if not, a push in the right direction.

 

 

 

Here are the 2 problems:

 

 

 

Econ 305, problem set 6

 

 

 

 

 

Question 1

 

 

 

Suppose that the economyÃÆââââ¬Å¡Ã¬Ã¢ââ¬Å¾Ã¢s production function is given by Y = K^(1/3) * L^(2/3)

 

(K raised to the one-third times L raised to the two-thirds)

 

 

 

and that both the saving rate, s, and the depreciation rate, ÃÆýÃâô , are equal to 0.10.

 

 

 

a) What is the steady-state level of capital per worker?

 

 

 

B) What is the steady-state level of output per worker?

 

 

 

Suppose that the economy is in steady state and that in period t, the depreciation rate increased from 0.10 to 0.20 permanently.

 

 

 

c) What will be the new level of steady-state capital per worker and output per worker?

 

 

 

d) Compute the path of output per worker and capital per worker over the first three periods after the change in the depreciation rate.

 

 

 

 

 

Question 2

 

 

 

Suppose that economy's production function is given by:

 

Y = K^(1/2) * (AN)^(1/2)

 

 

 

(k raised to the one-half, times AN raised to the one-half)

 

 

 

a) Are there decreasing returns to capital?

 

B) Transform the production function into a relation between output per effective worker and capital per effective worker.

 

c) Suppose that the growth rate of capital is 0.02, the growth rate of labor is 0.02 and the growth rate of the technological progress is 0.04. What is the growth rate of output?

 

d) Suppose that the saving rate, s, is 0.16, the depreciation rate ÃÆýÃâô is 0.1, the number of workers grows at 0.02 and the growth rate of technological progress is 0.04. Find the Steady State capital per effective worker, the steady state output per effective worker and the growth rate of output per effective worker.

 

e) Suppose now the growth rate of technological progress is 0.08. Redo part d.

 

 

 

 

 

 

 

 

 

Ok. Still with me? Here is what I have come up with so far.

 

 

 

#1. a. 1

 

b. 1

 

c. Steady-state capital per worker: 0.9

 

I found this by taking K1/N - K0/N = s[cubed root of K0/N] - ÃÆýÃâô [K0/N]. K1/N (Capital in period 1) is unknown. (What we are trying to find). K0/N (Capital in period 0) is 1. (Since it was in steady-state previously. So, this boils down to K1/N - 1 = [(0.1)(Cubed root of 1)] - [(0.2)(1)] which equals -.1. So, 1 - -0.1 = 0.9

 

 

 

Steady-state output of worker: 0.9654 (Found by taking the cubed root of 0.9)

 

 

 

d. Following the formula Kt+1/N - Kt/N = s[cubed root of Kt/N] - ÃÆýÃâô[Kt/N] (Capital in period t + 1 minus capital in period t is equal to the savings rate s times the cubed root of capital in period t, minus depreciation rate ÃÆýÃâô times capital in period t.)

 

 

 

Following this formula, I arrived at Kt+1/n = .8165. Kt+2/N = .7466 Kt+3/N = .688

 

 

 

 

 

 

 

#2 a. Yes. (I do not fully understand why, this is what it says in the book though.)

 

b. (K^1/2)/((AN)^(1/2)), or squared root of K over squared root of AN.

 

c. 0.06 (Found by adding gN and gA (Growth rate of labor with growth rate of technological progress.)

 

d. This is where I start to fall apart. I am not quite sure on how to approach this. Any help?

 

 

 

 

 

Once again, I am not asking for the answers. I am merely trying to get input on how I am doing....Am I headed in the right direction? On #2, part d (and ultimately e) do I redo what I was doing in #1, part d, but with the added technological progress?

 

 

 

Thanks,

 

 

 

Bobby

[death666bl00ms]

Also,

 

 

 

Notes for Chapters 11 and 12 (The chapters this particular homework is from) can be found at the following link (my course web page):

 

 

 

http://www.econ.umd.edu/~abozaid/econ305/

[indy500fan]

You'd be better off posting this on an economics related forum, the chances of someone here taking third year economics isn't very high.

[Sly_Wizard]

Did you make a typo? You say your production function is:

 

 

 

Y = K^(2/3) * L^(2/3)

 

 

 

Is one of those supposed to be 1/3?

 

 

 

Anyway... I'll help you with 1c as you have it written. You're going to have to rewrite your function in terms of the steady state of capital per worker. That'll be:

 

 

 

s(K^1/3) = ÃÆýÃâôK

 

 

 

Solve for K:

 

 

 

(s/ÃÆýÃâô)^3 = K

 

 

 

Substite for s and ÃÆýÃâô:

 

 

 

(.10/.20)^3 = K

 

 

 

K = .125

 

 

 

(Someone double check my work. I probably made a mistake somewhere. I took the question to say that at some unspecified point in the future that depreciation will rise from .10 to .20. Therefore I solved the function as I did in question 1a, but with the increased depreciation rate.)

[death666bl00ms]

Did you make a typo? You say your production function is:

 

 

 

Y = K^(2/3) * L^(2/3)

 

 

 

Is one of those supposed to be 1/3?

 

 

 

I did. My apologies. It should be K^(1/3).

[quitthegame]

Well I don't see how me railing against the use of diffy q's to model complex dynamics systems in a naive fashion gets you to ask me to help you do exactly that-- but I might as well try, see if I remember anything about them.

 

 

 

2.a) It's a decreasing return on capital because the function is Y = K^(1/2)*AN^(1/2) ... increasing return on capital would mean the exponent on K would be greater than 1.

 

 

 

B) got the same as you

 

 

 

c) My understanding is that you can't just add GsubA and GsubN like that, since the capital growth isn't keeping up with the effective workers. I get the growth rate of sqrt(12) / 100 ... yea steady state would require GsubK of .06 to match GsubA + GsubN. I just multiplied the growth rates through using the formula Y = (K)^(1/2) * (AN)^(1/2), seems like that should work but i'm not sure.

 

 

 

d) this is a steady state question, and part d of question 1 is not a steady state question, so no, i wouldn't recommend just redoing your work from question 1 with added tech. progress.

[death666bl00ms]

Well I don't see how me railing against the use of diffy q's to model complex dynamics systems in a naive fashion gets you to ask me to help you do exactly that-- but I might as well try, see if I remember anything about them.

 

 

 

2.a) It's a decreasing return on capital because the function is Y = K^(1/2)*AN^(1/2) ... increasing return on capital would mean the exponent on K would be greater than 1.

 

 

 

B) got the same as you

 

 

 

c) My understanding is that you can't just add GsubA and GsubN like that, since the capital growth isn't keeping up with the effective workers. I get the growth rate of sqrt(12) / 100

 

 

 

Of course...I should have known 2a. Thats like, common sense :oops:

 

 

 

2c, however, I was going off of what was said in the book and on the slides. However, looking back, it says that is for steady state. How did you come up with square root of 12/100?