Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(11,72) = In z1 + In I2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf , v£) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction ß of her day producing meat and the rest producing berries then her output is (vỉ, vž) = (38, 12(1 – B)). Which of the following statements is correct? O a. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and p units of good 2 (berries). Each agent of type g demands 6/p units of good 1 (meat) and 6 units of good 2 (berries). O b. Given equilibrium price p, each agent of type h demands 1/p unit of good 1 (meat) and 1 units of good 2 (berries). Each agent of type g demands 6 units of good 1 (meat) and 6/p units of good 2 (berries). O c. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and one units of good 2 (berries). Each agent of type g demands six units of good 1 (meat) and six units of good 2 (berries). O d. Given equilibrium price p, each agent of type h demands 6/p units of good 1 (meat) and 6 units of good 2 (berries). Each agent of type g demands one unit of good 1 (meat) and p units of good 2 (berries).
Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(11,72) = In z1 + In I2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf , v£) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction ß of her day producing meat and the rest producing berries then her output is (vỉ, vž) = (38, 12(1 – B)). Which of the following statements is correct? O a. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and p units of good 2 (berries). Each agent of type g demands 6/p units of good 1 (meat) and 6 units of good 2 (berries). O b. Given equilibrium price p, each agent of type h demands 1/p unit of good 1 (meat) and 1 units of good 2 (berries). Each agent of type g demands 6 units of good 1 (meat) and 6/p units of good 2 (berries). O c. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and one units of good 2 (berries). Each agent of type g demands six units of good 1 (meat) and six units of good 2 (berries). O d. Given equilibrium price p, each agent of type h demands 6/p units of good 1 (meat) and 6 units of good 2 (berries). Each agent of type g demands one unit of good 1 (meat) and p units of good 2 (berries).
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.11P
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Transcribed Image Text:Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and
they have the same preferences over consumption, represented by the utility function: u(x1, 22) = In r1 + In #2. However, there are twice as
many type-h agents as type-g agents.
The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest
producing berries then his output is (yf, y ) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction B of
her day producing meat and the rest producing berries then her output is (v7, y2) = (38, 12(1 – B)).
Which of the following statements is correct?
a. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and p units of good 2 (berries). Each agent of type g
demands 6/p units of good 1 (meat) and 6 units of good 2 (berries).
O b. Given equilibrium price p, each agent of type h demands 1/p unit of good 1 (meat) and 1 units of good 2 (berries). Each agent of type g
demands 6 units of good 1 (meat) and 6/p units of good 2 (berries).
O c. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and one units of good 2 (berries). Each agent of type
g demands six units of good 1 (meat) and six units of good 2 (berries).
O d. Given equilibrium price p, each agent of type h demands 6/p units of good 1 (meat) and 6 units of good 2 (berries). Each agent of type g
demands one unit of good 1 (meat) and p units of good 2 (berries).
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