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課程名稱︰總體經濟學（上）
課程性質︰英文授課
課程教師︰蔡宜展
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）2017/10/27︰
考試時限（分鐘）：3小時
試題 :
1. Nominal GDP vs Real GDP
Think about a simple economy that produces only 2 goods in the economy
(denoted by A and B).The table shows the hypothetical prices(p) and
quantities(q) of these good in 2005, 2006, and 2007.
========================================
| T| P_A| Q_A| P_B| Q_B|
|======================================|
| 2005| 1| 100| 2| 50|
|======================================|
| 2006| 1| 200| 2| 100|
|======================================|
| 2007| 2| 200| 4| 100|
========================================
1. Compute the nominal GDP and constant price real GDP for each year
using 2005 as the base year
2. Compute the implicit price deflator for each year using constant
price real GDP.
3. Compute the growth rate of nominal GDP, constant price real GDP
and the GDP deflator in 2006 and 2007. For each year indentify the
variable that does not change, explain why your answer makes sense.
4. Compute the value of the chain-weighted GDP using 2005 as the base
year.
5. Compute the implicit price deflator for each year using chain-
weighted real GDP.
6. Compute the growth rate of chain-weighted real GDP and its
associated GDP defaltor in 2006 and 2007. Compare these numbers with
the ones computed using constant price GDP. Is there any difference
between these numbers realtive to their constant price GDP counterpart?
2. Who is who in 2017
1. Who is the chairman of the Federal Reserve Bank?
2. Who was awarded the Nobel Prize in Economics in 2017? He/She was
awarded for his contribution in which area of Economics?
3. Solow Model
Let L_t denote the number of total population in period t, which is constant
over time. Each person has one unit of time that they supply as labor in each
period. Therefore, total labor supply is L_t. In addition each person consumes
a constant fraction, 1-s, of its income. Therefore the aggregate consumption
C_t equals the constant fraction of aggregate income Y_t, i.e. C_t=(1-s) * Y_t.
Furthermore, the aggregate saving in period t is S_t=s * Y_t. Suppose that
output is produced according to the constant returns to scale production
function Y_t=z * F(K_t,L_t)=z * K_t^a * L_t^(1-a) where K_t and L_t represent
the capital and labor input respectively. In addition, the law of motion for
capital stock evolves according to K_t+1=(1-δ)K_t+I_t. Finally, the equilibrium
condition required I_t=S_t.
1. Does this production functio satisfy consant returns to scale?
Explain.
2. Define y as output per worker, and k as captal per worker. Express
the relation between y and k.
3. Derive the law of motion for capital per capita, express the
relation in terms of saving rate and depreciation rate. In this
economy, what is break-even investment(the amount of investment needed
to keep capital per worker constant)?
4. Compute the steady-state quantity of capital per worker as a
function of the saving rate, the depreciation rate and total factor
productivity.
5. Use a diagram to show the effect of an increase in saving rate,
s, in the Solow Growth Model. In particular, please show both the
original and new steady state quantity of capital per capita in the
diagram, and explain dynamic adjustment of capital per worker over
time.
6. Now consider the economy with population growth and suppose its
growth is L_t+1=L_t(1+n). Derive the law of motion for capital per
worker. In this economy, what is break-even investment (the amount of
investment needed to keep capital per worker constant)?
7. Compute the steady-state quantity of capital per worker as a
function of the saving rate, population rate, the depreciation rate
and total factor productivity. Is the new steady state capital per
capita higher or lower relative to its constant population
counterpart?
8. Now suppose that there are two countries in the world. Assume that
country A and country B have the same production function, population
growth rate, depreciation rate and saving rate. Assume further that
country A have lower output per capita, which country has higher
growth rate in output per capita during the transitional dynamics?
Which country has higher growth rate in output per capita when r
eaching the steady state ?Explain?
9. Now consider the following production function
Y= F(K,E,L) = K^α*(EL)^(1-α). Where E denotes the efficiency of labor
. Suppose that labor efficiency improves over time where
E_t+1 = E_t(1 + g).Derive the relationship between output per
effective labor and capital per effective labor.
10. Derive the law of motion for capital per effective labor. What is
break-even investment (the amount of investment needed to keep
capital per worker constant) in this economy?
11. In the economy with population growth and labor efficiency
improvement, what would the steady state growth rate you predict
for the following variables?
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