Problem 1. Andy (consumer A) and Red (consumer B) growing old together on a remote island on which only fish (good 1) and coconut (good 2) are available for consumption. Both Andy and Red have Cobb-Douglas preferences. That is, consumer i has u(xi, z) = (a)¹/2 (1)¹/2, where x is consumer i' s good j consumption with j = 1, 2. Also, Andy's ini- tial endowment is w (w, w) (1,3) while Red's initial endowment is w = (wi, wz) = = = = (3, 1). (a) Draw the Edgeworth box for this economy. Mark the point indicating the initial endowment of each consumer. (b) Draw the contract curve for this economy in an Edgeworth box (a graphical represen- tation is sufficient). Explain if it is Pareto efficient for Andy and Red to consume their endowments. (c) What is the set of allocations that could be the outcome under barter in this economy? (d) Let the price of fish be p₁ while the price of coconut be normalized to 1 without loss of generality. For each consumer, solve the utility maximization problem, i.e., derive z for j= 1, 2 and i = A, B as a function of the price p₁. (e) Suppose p₁2. Draw the budget set for both Andy and Red, and show their optimal consumption bundles on the Edgeworth box. Can the economy be in equilibrium when P₁ = 2? (f) Calculate the equilibrium prices and demands for the economy. Show the equilibrium outcome on the Edgeworth box. (g) Plot the offer curve for consumer A. What happens to his consumption of good 1 and good 2 as the price p₁ increases? Plot also the offer curve of consumer B. Graphically, find the intersection of the two offer curves. What does this intersection signify? (h) Can you calculate the equilibrium price as a function of the initial endowments w's?
Problem 1. Andy (consumer A) and Red (consumer B) growing old together on a remote island on which only fish (good 1) and coconut (good 2) are available for consumption. Both Andy and Red have Cobb-Douglas preferences. That is, consumer i has u(xi, z) = (a)¹/2 (1)¹/2, where x is consumer i' s good j consumption with j = 1, 2. Also, Andy's ini- tial endowment is w (w, w) (1,3) while Red's initial endowment is w = (wi, wz) = = = = (3, 1). (a) Draw the Edgeworth box for this economy. Mark the point indicating the initial endowment of each consumer. (b) Draw the contract curve for this economy in an Edgeworth box (a graphical represen- tation is sufficient). Explain if it is Pareto efficient for Andy and Red to consume their endowments. (c) What is the set of allocations that could be the outcome under barter in this economy? (d) Let the price of fish be p₁ while the price of coconut be normalized to 1 without loss of generality. For each consumer, solve the utility maximization problem, i.e., derive z for j= 1, 2 and i = A, B as a function of the price p₁. (e) Suppose p₁2. Draw the budget set for both Andy and Red, and show their optimal consumption bundles on the Edgeworth box. Can the economy be in equilibrium when P₁ = 2? (f) Calculate the equilibrium prices and demands for the economy. Show the equilibrium outcome on the Edgeworth box. (g) Plot the offer curve for consumer A. What happens to his consumption of good 1 and good 2 as the price p₁ increases? Plot also the offer curve of consumer B. Graphically, find the intersection of the two offer curves. What does this intersection signify? (h) Can you calculate the equilibrium price as a function of the initial endowments w's?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Transcribed Image Text:Problem 1. Andy (consumer A) and Red (consumer B) growing old together on a remote
island on which only fish (good 1) and coconut (good 2) are available for consumption.
Both Andy and Red have Cobb-Douglas preferences. That is, consumer i has u(xi, z) =
(a)¹/2 (1)¹/2, where x is consumer i' s good j consumption with j = 1, 2. Also, Andy's ini-
tial endowment is w (w, w) (1,3) while Red's initial endowment is w = (wi, wz) =
=
=
=
(3, 1).
(a) Draw the Edgeworth box for this economy. Mark the point indicating the initial
endowment of each consumer.
(b) Draw the contract curve for this economy in an Edgeworth box (a graphical represen-
tation is sufficient). Explain if it is Pareto efficient for Andy and Red to consume their
endowments.
(c) What is the set of allocations that could be the outcome under barter in this economy?
(d) Let the price of fish be p₁ while the price of coconut be normalized to 1 without loss
of generality. For each consumer, solve the utility maximization problem, i.e., derive
z for j= 1, 2 and i = A, B as a function of the price p₁.
(e) Suppose p₁2. Draw the budget set for both Andy and Red, and show their optimal
consumption bundles on the Edgeworth box. Can the economy be in equilibrium when
P₁ = 2?
(f) Calculate the equilibrium prices and demands for the economy. Show the equilibrium
outcome on the Edgeworth box.
(g) Plot the offer curve for consumer A. What happens to his consumption of good 1 and
good 2 as the price p₁ increases? Plot also the offer curve of consumer B. Graphically,
find the intersection of the two offer curves. What does this intersection signify?
(h) Can you calculate the equilibrium price as a function of the initial endowments w's?
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