II Short Answer Questions
1. Growth Accounting
Assume that the production function of Taiwan during the Qing Dynasty is
given by:
𝑌 = 𝐴 × 𝑁 0.4 × 𝐿0.6
where: Y represents total output, A represents agricultural technology, L
represents the labor force, and N represents cultivated land area.
Given the following information:
• The growth rate of 𝐿 is 2%.
• The growth rate of 𝐴 is 0.25 of the growth rate of 𝑌 .
• The growth rate of 𝐿/𝑁 (i.e., the population density per unit of cultivated
land) is 0.5%.
9
Questions:
(a) Find the growth rate of cultivated land area 𝑁 .
In g
gF
>
-
In92-IngN
=
92-9N
=
a5 %
2
=
% - 9N
1 5% #
gN
(b) Find the growth rate of total output 𝑌 .
=
In gy
>
-
gy
=
=
=
.
Inga + 41ngN + ab Ing
a.
9a + 0 49N + 692
01259y + 0 4(1 5%) + 0 6(2 % )
.
.
94-0 259y
.
(c)
0.
.
=
0
.
6 % +1
.
2
.
%
>
-
algy
Find the growth rate of per capita labor productivity 𝑦 = 𝑌𝐿 .
In gy
>
-
gy
=
Ingy-Ing
=
gy-92
=
2 .
=
4%
-
04 %
4
2%
#
=
%>
1 8
.
-
97
=
2.
2. Job Search and Frictional Unemployment
Amy is looking for a job. Each month, she can interview with one company,
which will offer her a certain amount of monthly salary(月薪). If she accepts
the offer, she will keep earning that salary for a lifetime (assuming an infinite
horizon). If she declines, she will receive an unemployment benefit of $50
for that month and wait for the next interview opportunity in the following
1
month. The interest rate 𝑟 is such that 1+𝑟
= 0.9. This month, Amy receives
0 91
0 1
an offer of $70.
1
a9(+ r)
=
.
=
1 = 0. 9 + 0 9
(a) What is the definition of frictional unemployment?
.
r=
.
I
T
&
Frictional unemployment refers to the temporary unemployment that occurs when workers are
transitioning between jobs, entering the workforce for the first time, or re-entering after a period of
absence.
F
(b) If Amy take the offer of $70 monthly salary for the rest of her life, what is
the present value of her lifetime income (assuming an infinite horizon)?
n +y
+
.
-
=
%0
=
10
(
+
chr + City
H "H+
+
=
+
10x
,
·
)
in
x
+
=
y
=
70x9
=
6304
Suppose that she knows that if she declines the offer, the next month’s
offer will be $100 with a 50% probability and $50 with a 50% probability.
Additionally, her mother is forcing her to start working next month,
meaning she must accept whatever offer she receives then.
(c) What is the expected present value of her lifetime income if she declines
the offer this month? (remember the unemployment benefit of $50)
PEFEX
Y
FATE
( ) , FAI)
E $15
--
%
100 50 % + 50 50
-
PV
-
=
j
#R 67550
(RE)
=
5
=
607 5+ 50
.
=
657 5
#
.
15x9x9
=
b
(d) Suppose that Amy is risk neutral, will Amy accept the offer this month
or stay unemployed this month?
accept
the offer this
umemployed
stay
this
month
month
=
PV
:
PV
=
=
63
657 5
$657 57$630
.
"
Amy
will
Stay unemployed
6
this
mouth
.
3. Structural Unemployment
The following figure shows the demand and supply curves in the market for
workers (called “baristas”) in Starbucks coffee shops. The hourly wage in this
market has been fixed at $7.25 and cannot be changed.
(A) What is wage rigidity(薪資僵固性)? What are the reasons economists
believe wage rigidity occurs?
Wage rigidity refers to the situation where wages do not adjust quickly to
changes in labor market conditions, leading to involuntary unemployment.
· E,GENEXY NE , MILEEDIPE
PENE . DE E2 ,
_
(B) Suppose the labor market clears at the current wage of $7.25. Draw a
supply and demand diagram to illustrate this scenario.
P(wage)
$9 25
.
S
- - - -
I
D
·
a Cabor)
x
(C) Suppose that, due to concerns about the high number of calories in many
Starbucks drinks, the demand for Starbucks products declines. Use the
diagram to explain what will happen to employment in the market for
baristas.
Product Market (Starbucks drinks)
Labor Market
(Starbucks Baristas*** Y (Q1
Plwage)
S
StarbucksYYI
i
.
*XXI
& .
4---Tp
Dalar is
(D) Which type of unemployment describe the results in (c)?
(structural
7
(2)
,
E ,Wage $1 25 ==**
=
$3
-
unemployment
.