Consider an exchange economy with two agents, 1 and 2, and two goods, apples and bananas. The agents' preferences are represented by the utility functions U₁ (x₁, y₁) = x₁ + ln(1 + y₁), U₂ (X₂, Y₂) = x₂ + 2ln(1 + y₂), where In stands for the natural logarithm and, for i = 1, 2, x¡ denotes agent i's
Consider an exchange economy with two agents, 1 and 2, and two goods, apples and bananas. The agents' preferences are represented by the utility functions U₁ (x₁, y₁) = x₁ + ln(1 + y₁), U₂ (X₂, Y₂) = x₂ + 2ln(1 + y₂), where In stands for the natural logarithm and, for i = 1, 2, x¡ denotes agent i's
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Consider an exchange economy with two agents, 1 and 2, and two goods, apples and
bananas. The agents' preferences are represented by the utility functions
U₁ (x₁, y₁) = x₁ + ln(1 + y₁),
U₂ (X₂, Y₂) = x₂ + 2ln(1 + y₂),
where In stands for the natural logarithm and, for i = 1, 2, x; denotes agent i's
consumption of apples and y; denotes agent i's consumption of bananas. Before trade,
agent 1 owns 10 apples and 0 bananas while agent 2 owns 0 apples and 10 bananas.
(a) Describe all the efficient (i.e., Pareto optimal) allocations of this exchange
economy. Recall that not all agents need consume a strictly positive quantity of all
goods.
(b) Compute the competitive equilibrium of this exchange economy. Without loss
of generality, normalize the unit price of apples to 1, and denote the unit price of
bananas by p. What is the equilibrium price of bananas? What are the agents'
equilibrium consumptions of apples and bananas?
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