at the society's utility iven by: U = XY dY are two commodities e point on the PPF that tility. Calculate the utility vith this combination. che economy is now hternational trade. X and I on the basis of one unit -y unit of X [Hint: (Xp
at the society's utility iven by: U = XY dY are two commodities e point on the PPF that tility. Calculate the utility vith this combination. che economy is now hternational trade. X and I on the basis of one unit -y unit of X [Hint: (Xp
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![You are given the following
Production Possibility Frontier (PPF):
x2 + Y = 1728
Suppose that the society's utility
function is given by: U = XY
where X and Y are two commodities.
(a) Derive the point on the PPF that
maximises utility. Calculate the utility
associated with this combination.
(b) Assume the economy is now
opened to international trade. X and
Y are traded on the basis of one unit
of Y for every unit of X [Hint: (Xp
-Xc) = (Yc -Yp), where Xp and Yc
are the respective amounts of goods
X and Y produced while Xc and Yc
are the respective amounts of goods
X and Y consumed]. Write down the
constrained maximization problem
and solve for optimal production,
trade, and consumption.
(c) Show that utility has increased
with international trade.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0173021b-6362-4383-be96-00e4154fae41%2Fd323eeaa-d4fd-4f4a-afec-702e658256ce%2F766asc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:You are given the following
Production Possibility Frontier (PPF):
x2 + Y = 1728
Suppose that the society's utility
function is given by: U = XY
where X and Y are two commodities.
(a) Derive the point on the PPF that
maximises utility. Calculate the utility
associated with this combination.
(b) Assume the economy is now
opened to international trade. X and
Y are traded on the basis of one unit
of Y for every unit of X [Hint: (Xp
-Xc) = (Yc -Yp), where Xp and Yc
are the respective amounts of goods
X and Y produced while Xc and Yc
are the respective amounts of goods
X and Y consumed]. Write down the
constrained maximization problem
and solve for optimal production,
trade, and consumption.
(c) Show that utility has increased
with international trade.
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