Question

数学题 急求答案，拜托各位！！！

Consider the Solow model demonstrated in class.
(a) Write down a Cobb-Douglas production function and verify that it exhibits
constant returns to scale.
(b) We assumed a closed economy. In a closed economy, the total saving is
equal to the total investment, i.e., it holds that:
It = St. (1)
Why does this equation hold in a closed economy? Explain intuitively.
(c) Suppose that ct = (1 − s)yt where 0 < s < 1. In class, we obtained two
other equations as follows:
Yt = ctLt + St (2)
Kt+1 = It + (1 − δ)Kt. (3)
By using Eqs.(1), (2), and (3), derive a difference equation such that:
kt+1 =
sA
1 + n
kα
t +
1 − δ
1 + n
kt. (4)
(d) Derive per capita consumption (ˆc) and per capita capital (ˆk) in the steady
state.
(e) Investigate the signs of ∂ˆk
∂n and ∂ˆk
∂s .
(f) Derive the saving rate, s, that maximizes per capita consumption (ˆc) in
the steady state.

(g) Draw a phase diagram that illustrates the dynamic behavior of per capita
capital (kt).
(h) Suppose that δ = 1. Let gt+1 = yt+1
yt − 1. Then gt+1 is a growth rate of
output. Show that limkt→∞ gt+1 = −1, limkt→0 gt+1 = ∞, and ∂gt+1
∂kt
< 0.
(i) Do you think that the Solow model can explain income differences between
countries? Explain.
(j) Do you think that the Solow model can explain the high growth rates in
Japan after World War II. Consider the destruction of capital stock in Japan.
Question 2
(a) Show that (f(g(x)))0 = f0(g(x))g0(x).
(b) Show that ( f(x)
g(x) )0 = f0(x)g(x)−f(x)g0(x)
(g(x))2 .
(c) Show that (log x)0 = 1/x.

Answer 1

设油桃采了x斤，每斤y元，则由题可得：
樱桃采了(x-5)斤，每斤2y元，所以
可得：xy=80......(1)

(x-5)(2y)=80......(2)
由（2）得：2xy-10y=80，
将（1）带入上式得：2*80-10y=80，解得：y=8(元）
再代入（1）可解得：x=10(斤）
所以得：樱桃采了x-5=10-5=5(斤)

Answer 2

你水平太高，俺看不懂，您换的地方吧

嗯，最好说中国话

Answer 3

如果是中国人，最好用中文。

Answer 4

这是一个编程题，很多字母不会写呀，再说英文水平…