代写Assignment 4帮做Python语言程序

日期：2025-02-18 05:22

Assignment 4

1.    Consider two economies A and B with the following production functions:

YA(t) = KA(t)α   K(̇)A (t) = SAYA(t)

And

YB(t) = KB(t)α   K(̇)B (t) = SBYB(t)

Where α>1. Economies have the same initial value of K but,sA>sB  . Show that Y1/Y2  is continually rising.

2.    Consider the Knowledge accumulation model where:

Y(t) = A(t)(1 − aL )L(t)

And

A(̇)(t) = B[aLL(t)]YA(t)θ

Where θ < 1.

Population growth rate is constant at n.

Describe how each of the following affect thė(g) = 0 line and the growth rate of A at the moment of change and in the long run (graph Ln A overtime to show the effect).

a)   An increase inn.

b)   An increase in aL.

c)    An increase in ϴ .

3.    Suppose that output is given by the equation Y(t) = K(t)α [A(t)L(t)]1−α , that L is constant and equal to 1; thatK(̇)(t) = SY(t) and that knowledge accumulation occurs as aside effect of goods  production:A(̇)(t) = BY(t).

a.    Find expression for gA(t) and gK(t) in terms of A(t), K(t) and parameters of the model.

b.    Sketch the ġA  = 0 and ġk  = 0 lines in (gA,  gK) space.

c.    Does the economy converge to a balanced growth path? If so, what are the growth rates of K, A and Y on the balanced growth path?

d.    How does an increase in s affect long-run growth rate?

4.    Consider the  model  with education where  G(E) = e ∅E  and  Y(t) = K(t)α [A(t)H(t)]1−α   and H(t) = L(t)G(E)  and  A(̇)(t) = gA(t)  and  L(̇)(t) = nL(t)  and  constant  depreciation  rate  of  δ . However, assume that E rather than being constant is increasing steadily: E(̇)(t) = mwhere m>0. With this change what is the long-run growth rate of output per worker?

5.  Suppose  that output is given by the  equation Y(t) = K(t)α [(1 − aH )H(t)]β  , H(̇)(t) = BaHH(t) andK(̇)(t) = SY(t).

Assume 0<α<1 , 0<β<1 and α+β>1.

a.    What is the growth rate of H?

b.    Does the economy converge to a balanced growth path? If so, what are the growth rates of K and Y on the balanced growth path?