Question

Imagine an economy makes only clothes (QC) and food (QF) and has two inputs of production: Labor (L) and Capital (K). It takes 4 units of capital and 1 unit of labor to make one unit of clothing. It takes 1 unit of capital and 1 unit of labor to make one unit of food. There is no substitutability between the two inputs.

**Hint: the total cost of production, TC, is equal to the
wL+rK. You can think of L and K in this context as the number of
units of Labor or Capital that it takes to make one unit of the
good.**

a. Write down the unit cost of production for one unit of clothing and one unit of food as a function of the wage (w) and rental rate (R). In a competitive market, those costs will be equal to the prices of clothing (PC) and food (PF), so write equations that set the price of the good equal to the cost of producing it.

b. Use the two equations in part (a) to solve for equations for w and R in terms of PC and PF(hint: you have two equations and two unknowns. This will take some algebra).

c. Before trade, the no-trade prices are Pc=$35 and PF=$20. Calculate w and R.

d. When trade opens, Home exports QC and the world prices are Pc=$39 and PF=$15. Calculate w and R again under the world prices. Compare them to what you found in part (c). How is this consistent with the Heckscher- Ohlin Model?

Answer #1

Consider our usual setting with two goods (food and
clothing) and two inputs (capital and labor). Units of
labor and capital respectively needed to produce one unit of food
are given by LF = 4, KF = 1, meaning that
you need 4 units of labor and 1 unit of capital to produce 1 unit
of food. The input requirements to produce
one unit of clothing are given by LC = 1, KC = 2. Denote LC and KC
as...

A hat manufacturing ﬁrm has the following production function
with capital and labor being the inputs: Q = min(5L,3K) (it has a
ﬁxed-proportions production function). If w is the cost of a unit
of labor and r is the cost of a unit of capital, derive the ﬁrm’s
optimal inputs, long-run total cost curve, average cost curve, and
marginal cost curve in terms of the input prices and Q.
b) A ﬁrm has the linear production function Q = 2L...

2. Use the specific-factors model to answer question 2. Assume
that there are two industries, food and cloth. The food industry
uses labor and land as inputs while the cloth industry uses labor
and capital as inputs. The marginal product of labor in both
industries is as follows:
Marginal Product of Labor
Labor
Cloth
Food
0
1.4
1.6
1
1.3
1.5
2
1.2
1.4
3
1.1
1.3
4
1
1.2
5
.9
1.1
6
.8
1
7
.7
.9...

Consider the following data on quantities of two factors,
capital and labor, available, and their use to produce a unit of
each of the two goods, cloth and food: K = 3000,
L = 2000, aKC = 2,
aLC= 2, aKF = 3,
aLF = 1.
a. Derive equations for
PC and PF. Now solve the
equations for w (wage rate) and r (capital rental
rate). (No need to write the expressions on the answer space
provided). Answer the following questions...

Consider a firm for which production depends on two normal
inputs, labor and capital, with prices w and r, respectively.
Initially the firm faces market prices of w=4 and r=2. These prices
shift to w=8 and r=6.
In which direction will the substitution effect change the
firm’s employment and capital stock?
In which direction will the scale effect change the firm’s
employment and capital stock?
Can we say conclusively whether the firm will use more or less
labor? More or...

Consider a firm for which production depends on two normal
inputs, labor and capital, with prices w and r, respectively.
Initially the firm faces market prices of w=4 and r=2. These prices
shift to w=8 and r=6.
In which direction will the substitution effect change the
firm’s employment and capital stock?
In which direction will the scale effect change the firm’s
employment and capital stock?
Can we say conclusively whether the firm will use more or less
labor? More or...

QUESTION 2
The textbook considers the extension of the Ricardian model to
more than two goods – let’s consider the case of more than two
countries.
Consider a world of FIVE countries: two countries (A, B, C, D
and E), that produce clothing and food with one factor of
production, labor. Suppose the opportunity cost of clothing with
respect to food (aLC/ALF) in each country is
the following:
A: 1 B: 2 C: 3
D:4 E:5
Suppose the international...

Comparative Advantage
There are two countries in the world.
There are also only two different types of goods produced, food and
clothing. Each country has the same amount of “inputs” (i.e. labor,
capital, raw materials, etc.), which amounts to 100,000 units of
input. Below is a chart that lists out how many units of output
each country could create if they created just one type of good.
For example, if Country A produced ONLY food, then with 100,000
units of...

Consider a two countries, Portugal and England, that produce two
goods, wine and cheese, with only one factor of production, Labor.
In Portugal, one unit of labor can produce 1 unit of wine or 1 unit
of cheese. In England, one unit of labor can produce 1 unit of wine
or 2 of cheese. There are 100 units of labor in Portugal, and 100
in England. Countries share the same tastes, and there is perfect
competition.
1) Fill in the...

) Consider Home produces computers(C) and food(F) using
capital(C) and labor(L). The unit factor requirements are fixed and
given by: aLC = 2, aKC = 6, aLF = 3, aKF = 4. The total labor
supply is 900 and the total capital stock is 1,500. (1 point) a.
Which good is relatively labor intensive? Which good is relatively
capital intensive? (2 points) b. Derive and draw the PPF of this
country. At which point on the PPF are both factors...

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