UA(XA. YA) = 4XA + 3YA UB (XB. Ya) 5(X)^ (Y₂)² Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer B has 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Py be the prices of goods X and Y, respectively. Write down expressions for the two individuals' budget constraints.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Question 1:
Consider a pure exchange economy with two consumption goods, X and Y, and two
consumers, A and B. There are 20 units of X and 20 units of Y in the economy. The
preferences of the consumers are represented by the following utility functions:
UA(XA, YA) = 4XA + 3YA
of 3
UB (XB, YB) = 5(XB)4 (YB)²
Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer B
has 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Pybe the prices
of goods X and Y, respectively. Write down expressions for the two individuals' budget
constraints.
Transcribed Image Text:Page < 2 Question 1: Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B. There are 20 units of X and 20 units of Y in the economy. The preferences of the consumers are represented by the following utility functions: UA(XA, YA) = 4XA + 3YA of 3 UB (XB, YB) = 5(XB)4 (YB)² Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer B has 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Pybe the prices of goods X and Y, respectively. Write down expressions for the two individuals' budget constraints.
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What are the values of PX and PY in the general competitive equilibrium of this
economy? Why?

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ketch the indifference curves and the initial allocation on an appropriate diagram. In
your diagram identify the area where there is scope for a Pareto improvement and explain why
this is the case.

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