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THIS WAS HOMEWORK 4. WHICH HAS ALREADY BEEN TURNED IN, NOW I NEED HELP WITH 5 Your answers must be placed in separate papers.
THIS WAS HOMEWORK 4. WHICH HAS ALREADY BEEN TURNED IN, NOW I NEED HELP WITH 5
Your answers must be placed in separate papers. Before you turn in your homework,
you must place the homework sheet on top of your other papers and must have them stapled
altogether. Your answers must be well structured in order. You will lose 25% of your score if
you do not follow these instructions. Any duplicated work from other students is absolutely not
acceptable.
Problem
. Home is an economy endowed with three production factors: labor (
L
), capital (
K
) and
land (
T
). Home can produce cloth (
Q
C
) with labor and capital, while producing food (
Q
F
) with
labor and land. In this economy, labor is a mobile factor between the cloth and food industries. In
contrast, capital is specific to the cloth industry, while land is specific to the food industry. Home's
utility function, cloth production function, food production function are, respectively, given by
U
(
D
C
,D
F
) =
D
λ
C
D
1
−
λ
F
Q
C
=
AK
α
L
1
−
α
C
Q
F
=
AT
α
L
1
−
α
F
where
L
C
is labor used for cloth production,
L
F
is labor used for food production, and the param-
eters are
λ
= 0
.
40
,
A
= 100
, α
= 0
.
3
,
K
= 200
,
T
= 300
,
L
= 1000
. Home is in autarky.
a) Calculate the equilibrium employment of labor in each industry. You must show your calculation.
(10 pts)
b) Calculate the equilibrium output levels of cloth and food. You must show your calculation. (10
pts)
c) What is the equilibrium consumption of cloth and food? Why? (10 pts pts)
d) Show why the equilibrium relative price of cloth, as measured by
P
C
P
F
, is actually reflected in the
ratio of the marginal labor productivity in food production to the marginal productivity of labor
in cloth production, and calculate the equilibrium relative price of cloth. (10 pts)
e) Calculate real GDP in terms of cloth and food, respectively. Show your calculation. (10 pts)
f) Calculate real wage in terms of cloth and food, respectively. Show your calculation. (10 pts)
g) Calculate real reward to capital owners in terms of cloth and food, respectively. Show your
calculation. (10 pts)
h) Calculate real reward to land owners in term of cloth and food, respectively. Show your calcu-
lation. (10 pts)
i) Based on your numerical results calculated above, plot the following two graphs:
•
The labor market equilibrium. You must label this graph clearly with your numerical results.
(10 pts)
•
The utility maximization and production equilibrium. You must label this graph clearly
with your numerical results. [Hint: the graph should include PPF, Budget Line, and Utility
Curve.] (10 pts)
HOMEWORK 5 IS BELOW
nstructions
: Your answers must be placed in separate papers. Before you turn in your homework,
you must place the homework sheet on top of your other papers and must have them stapled
altogether. Your answers must be well structured in order. You will lose 25% of your score if
you do not follow these instructions. Any duplicated work from other students is absolutely not
acceptable.
Problem
. Home is an economy endowed with three production factors: labor (
L
), capital (
K
) and
land (
T
). Home can produce cloth (
Q
C
) with labor and capital, while producing food (
Q
F
) with
labor and land. In this economy, labor is a mobile factor between the cloth and food industries. In
contrast, capital is specific to the cloth industry, while land is specific to the food industry. Home's
utility function, cloth production function, food production function are, respectively, given by
U
(
D
C
,D
F
) =
D
λ
C
D
1
−
λ
F
Q
C
=
AK
α
L
1
−
α
C
G
F
=
AT
α
L
1
−
α
F
where
L
C
is labor used for cloth production,
L
F
is labor used for food production, and the param-
eters are
λ
= 0
.
40
,
A
= 100
, α
= 0
.
3
,
K
= 200
,
T
= 300
,
L
= 1000
. Home is in autarky. On
Homework 3, you had computed Home's autarkic equilibrium.
a) From your Homework 4, tabulate your computed results based on
L
C
,
L
F
,
Q
C
,
Q
F
,
D
C
,
D
F
,
P
C
P
F
, real
GDP
, real rewards to labor, capital, and land. Note that you just need fill out the the
table you make without showing your calculations. For these real values, you just need to show
them in terms of food. (10 pts)
b) Home has a comparative advantage in cloth production, compared to the rest of the world. If
Home is no longer an autarkic economy and trades with the rest world, the relative price of cloth
made in Home must therefore jump up. Let us assume that under free trade this relative price will
jump up by 10% from the autarkic level. To see how free trade will impact the home economy, you
are asked to compute: (i)
L
C
,
L
F
, (ii)
Q
C
,
Q
F
, (iii)
D
C
,
D
F
, (iv) real
GDP
, and (v) real rewards
to labor (
L
), capital (
K
) and land (
T
). These real values must be measured by units of food. You
must show your computations. (40 pts)
c) Make an extended table to summarize your computed results for both the autarkic and free-trade
equilibria. The suggested able form is given below:
Variable
Autarky
Free Trade
Percent Change
L
C
L
F
where the percent-change column is for you to show the percent change in the corresponding variable
from autarky to free trade. (10 pts)
d) From the tabulated results of (c), analyze how free trade impacts Home in terms of resource
reallocation and specialization. (10 pts)
e) From the tabulated results of (c), analyze whether capital owners, or land owners, or workers
are better off, worse off, or whatever. (10 pts)
f) Compute Home's welfare under autarky and free trade and explain whether Home can gain from
trade. (10 pts)
g) Graph the change in the labor market equilibrium based on the tabulated results of (3). (10 pts
