課程名稱︰總體經濟學一
課程性質︰系定必修
課程教師︰陳虹如
開課系所︰經濟系
試題 :
2.(25) An economy consists of two families, the Reds and Greens. Each family
owns a factory and produces output with the same technology. This technology
is
L^2
Y = f(L) = 48L－ ──
2
The Red family has preferences
U(C,48－L) = C－L^2 , L < = 48
The Green family has preferences
U(C,48－L) = C－L^2 , L < = 48
Where L is working time and total hours of time is 48.Answer the following
questions :
dU dU
(a)(4)Find an expression for the slope of an indifference curve(-─/─)
dL dC
of the Red family. Do the same exercise for the Green family.
(b)(6)If each family allocates its time to produce using its own factory,
how much time will each family allocate to production?
(c)(4)Calculate the productivity of the economy ; this is measured as
Y_red ＋ Y_green
Productivity = ──────────
L_red ＋ L_green
(d)(4)Assume that the economy is run by a benevolent social planner who owns
both factories and can allocate the labor of each family. We assume that the
social planner will set the slopes of the indifference curves for Red and Gre
-en families equal. Find the expression for the amount of Red family labor th
-e social planner will use relative to the amount of Green family labor. In
other words, find the value of the number “b” such that
L_green = bL_red
(e)(7) The social planner chooses to set the amount of labor in each factory
the same and equals L_avg = (L_red ＋ L_green)/2. The social planner will
also set the slope of an indifference curve for each family to the slope of
the production function for each factory. Using the result you get in (d),
find how much Red labor the social planner will use. What is the total output
in this economy?
3(23)Consider the Solow Growth Model
θ 1-θ
Y_t = AK_t(E_t,L_t) (1)
E_t+1 = (1+g)E_t , E_t = 1 , g > 0
L_t+1 = L_t = L , for all t
Y_t = C_t + I_t (2)
I_t = sY_t (3)
K_t+1 = I_t + (1-δ)K_t (4)
(a)(4)Divide each variable by E_tL_t,rewrite equation (1) (2) (3) and (4) in
terms of new variables.
(b)(4)Define k_t = K_t/(E_tL_t),solve for the steady state level of capital,
k^*, as a function of δ,s,θand g .
(c)(5) If k_t is at a the steady state, what are the growth rate of Y_t,C_t
and I_t ?
(d)(10) How many possible the steady state are there? What is the golden rule
, and how does it help use choose just one the steady state to consider? What
is the golden rule saving rate?
4.(12)Assume a representative agent only lives two periods (period 1 for being
young and period 2 for being old). Assume her income is 20 when she is young
and 0 when she is old. Suppose the interest rate is 2% and she want to smooth
her consumptions (that is consumptions in period 1 and period 2 are the same
).Answering the following questions:
(a)(3) What is her intertemporal budget constraint?
In the following problems (b),(c) and (d),calculate the answer until the
first digit of the decimal.
(b)(3) How much will she save?
(c)(3) If the government uses pay-as-you-go as the way of social security.
That means, young agents need to pay for social security for old people.
When this agent is young, she needs to pay 4 for the tax. But she will get 6
as the social security when she becomes old. What is her new intertemporal
budget constraint?
(d)(3) Follow from (c), how much will she save?
5.(10) Suppose that the government cuts taxes today, but leaves government
purchases unchanged and finances this spending with debt. According to the
Keynesian point of view, how will consumption today be affected by this
changed? According to the Ricardian view, how will consumption today be
affected by this changed? Explain your answers.
6.(Bonus!)(10) Given the production function Y = AK^αL^1-α, explain what is
growth accounting? According to Young (1994), what were main factors contribu
-te to learned from the Solow model, what advices you would suggest to these
countries to maintain high growth rates?
[終於完了Orz]
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