a) If labor and capital markets are perfectly competitive, what are the conditions (two for each sector) relating the amount of each factor employed in a sector to the price of the factor and the price of the product? Make sure to base your answer on the provided production functions. b) For each sector, combine the two conditions from (a) to obtain the capital/labor ratio Ki/Li in each sector i as a function of the wage/rental ratio w/r. Which good is labor-intensive? c) Use the results from a) and b) to derive the relationship between the relative price of goods Pc/Pp and the relative factor price w/r. [Hint: first get from a) a relation between the relative price of goods and the marginal products of, say, labor in the two sectors; write the marginal products in terms of Ki/Li; then from b) you know how Ki/L; depends on w/r...] Do you find a positive or a negative relationship?
a) If labor and capital markets are perfectly competitive, what are the conditions (two for each sector) relating the amount of each factor employed in a sector to the price of the factor and the price of the product? Make sure to base your answer on the provided production functions. b) For each sector, combine the two conditions from (a) to obtain the capital/labor ratio Ki/Li in each sector i as a function of the wage/rental ratio w/r. Which good is labor-intensive? c) Use the results from a) and b) to derive the relationship between the relative price of goods Pc/Pp and the relative factor price w/r. [Hint: first get from a) a relation between the relative price of goods and the marginal products of, say, labor in the two sectors; write the marginal products in terms of Ki/Li; then from b) you know how Ki/L; depends on w/r...] Do you find a positive or a negative relationship?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Heckscher-Ohlin:
Consider an economy with two goods (cornand potatoes), both produced using capital and labor. Both factors can freely move across sectors. The technologies for the two sectors are given by the following Cobb-Douglas production functions:
Transcribed Image Text:Qc = Ac Kc“ Lc"
1-a
Qp = Ap Kp Lp'
with 1>a> B> 0.
The allocation of labor and capital to the two industries is subject to the resource
constraints
Lc + Lp = L
and
Kc + Kp = K
where L and K are the aggregate endowments of labor and capital.
Prices of corn and potato are denoted by Pc and Pp, respectively. Prices for capital and
labor are denoted by R and W, respectively.
Consumers have Leontief preferences, utility function U(Cc, CP) = min(Cc, CP), meaning
that they want to consume the two goods in a fixed proportion of one-to-one (no
substitution).
![a) If labor and capital markets are perfectly competitive, what are the conditions
(two for each sector) relating the amount of each factor employed in a sector to
the price of the factor and the price of the product? Make sure to base your answer
on the provided production functions.
b) For each sector, combine the two conditions from (a) to obtain the capital/labor
ratio K/Li in each sector i as a function of the wage/rental ratio w/r. Which good
is labor-intensive?
c) Use the results from a) and b) to derive the relationship between the relative price
of goods Pc /Pp and the relative factor price w/r. [Hint: first get from a) a relation
between the relative price of goods and the marginal products of, say, labor in the
two sectors; write the marginal products in terms of K/Li ; then from b) you know
how K/L; depends on w/r...] Do you find a positive or a negative relationship?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ae73136-9df5-4db8-9008-250c2e6461dc%2Fda27a775-ae23-4001-8cb1-5f006795a999%2F76yzfld_processed.png&w=3840&q=75)
Transcribed Image Text:a) If labor and capital markets are perfectly competitive, what are the conditions
(two for each sector) relating the amount of each factor employed in a sector to
the price of the factor and the price of the product? Make sure to base your answer
on the provided production functions.
b) For each sector, combine the two conditions from (a) to obtain the capital/labor
ratio K/Li in each sector i as a function of the wage/rental ratio w/r. Which good
is labor-intensive?
c) Use the results from a) and b) to derive the relationship between the relative price
of goods Pc /Pp and the relative factor price w/r. [Hint: first get from a) a relation
between the relative price of goods and the marginal products of, say, labor in the
two sectors; write the marginal products in terms of K/Li ; then from b) you know
how K/L; depends on w/r...] Do you find a positive or a negative relationship?
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