Consider a world composed of two countries, Home (H) and Foreign (F). Individuals living in each country == H, F have preferences over two goods x and y. In each country there is only one factor of production, labour, which is perfectly mobile between industries but immobile between countries. The total labour endowment at Home is LH 10 and the total labour endowment in Foreign is LF 10. The marginal product of labour in each industry is constant. At Home, one worker can produce 2 units o good x or 1 unit of good y per unit of time; at Foreign one worker can produce 1 unit of good x or 2 units of good y per unit of time. Assume that consumers in Home and Foreign always consume goods x and y in the same quantity regardless =

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question

"Only answer c-d ones"

(a) Calculate the opportunity cost of producing one additional unit of good x in terms of units of good y in Home and Foreign.

The opportunity cost of producing one additional unit of good x in Home or foreign is the amount of good y that must be given up to produce it.

At Home, one worker can produce 2 units of good x or 1 unit of good y. Thus, to produce one additional unit of good x, half a unit of good y must be given up. The opportunity cost in Home is 0.5 units of good y. In Foreign, one worker can produce 1 unit of good x or 2 units of good y. To produce one additional unit of good x, two units of good y must be given up. The opportunity cost in Foreign is 2 units of good y.

(b) Derive the production possibilities frontier (PPF) for Home and Foreign and plot it in a graph with good x in the horizontal axis and good y in the vertical axis.

To derive the production possibilities frontier (PPF) for Home and Foreign, we use the labor market clearing condition in each country.

 

For Home, the total labor endowment is LH = 10. In Home, 1 worker produces 2 units of good x (xH) and 1 unit of good y (yH). The labor market clearing condition in Home is: LH = (xH / 2) + yH. Rearrange this equation to get yH in terms of xH: yH = 10 - (xH / 2).

 

For Foreign, the total labor endowment is LF = 10. In Foreign, 1 worker produces 1 unit of good x (xF) and 2 units of good y (yF). The labor market clearing condition in Foreign is: LF = xF + (yF / 2). Rearrange this equation to get yF in terms of xF: yF = 20 - 2 * xF.

 

Both PPFs are linear, with negative slopes. We Plot the Home PPF using the equation yH = 10 - (xH / 2) and the Foreign PPF using the equation yF = 20 - 2 * xF  to get the following graph below:

 

 

(c) Determine the equilibrium price of good x (setting the price of good y as 1) that prevails at Home and Foreign under autarky - that is, when they do not trade with each other. Explain why any other price could not be the equilibrium price in autarky. (USE profit maximising in each industruy at home and the relative price of x in autarky in a given country has to be equal to the slope of the PPF - the opportunity cost of producing one additional unit of good x, expressed in units of good y.)

 

(d) Determine the optimal consumption and production at Home and Foreign under autarky. Depict this situation in a graph that includes each country's PPF and indifference curves for the representative consumer. (To find the optimal consumption at Home simply maximise the representative consumer's utility subject to the PPF, noting that in autarky, consumption of each good has to be equal to domestic production. + The Lagrangian  and The F.O.C + Taking the ratio of the two)

(e) Assume that Home and Foreign open to trade with each other. Explain how is the pattern of trade (which good will each country export and import) determined (Use the the Ricardian model, the pattern of trade is determined by comparative advantage)

(f) Suppose that the equilibrium price of good x (keeping the price of good y as 1) is equal to 1. Determine the optimal production and consumption both at Home and Foreign when they open up to trade. Depict this in graph. 

 

 

 

 

 

Consider a world composed of two countries, Home (H) and Foreign (F). Individuals living in each country
i = H, F have preferences over two goods x and y.
In each country there is only one factor of production, labour, which is perfectly mobile between industries but
immobile between countries. The total labour endowment at Home is LH 10 and the total labour endowment
in Foreign is LF = 10.
=
The marginal product of labour in each industry is constant. At Home, one worker can produce 2 units of
good x or 1 unit of good y per unit of time; at Foreign one worker can produce 1 unit of good x or 2 units of good
y per unit of time.
Assume that consumers in Home and Foreign always consume goods x and y in the same quantity regardless
of their prices. That is, Cri = Cyi, i = H, F.
Transcribed Image Text:Consider a world composed of two countries, Home (H) and Foreign (F). Individuals living in each country i = H, F have preferences over two goods x and y. In each country there is only one factor of production, labour, which is perfectly mobile between industries but immobile between countries. The total labour endowment at Home is LH 10 and the total labour endowment in Foreign is LF = 10. = The marginal product of labour in each industry is constant. At Home, one worker can produce 2 units of good x or 1 unit of good y per unit of time; at Foreign one worker can produce 1 unit of good x or 2 units of good y per unit of time. Assume that consumers in Home and Foreign always consume goods x and y in the same quantity regardless of their prices. That is, Cri = Cyi, i = H, F.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

WHat are the graphs for both?

 

Solution
Bartleby Expert
SEE SOLUTION
Knowledge Booster
Production Possibility Frontier
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education