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Questions and Answers
What condition must be met for an allocation to be Pareto efficient in the context of an exchange economy?
What condition must be met for an allocation to be Pareto efficient in the context of an exchange economy?
An allocation is Pareto efficient if no agent can be made better off without making at least one other agent worse off.
How do utility functions help in understanding the behavior of economic agents?
How do utility functions help in understanding the behavior of economic agents?
Utility functions quantify the preferences of agents, helping to predict their choices based on the allocation of goods.
What is a blocking allocation, and why is it significant in determining core allocations?
What is a blocking allocation, and why is it significant in determining core allocations?
A blocking allocation is one where a coalition of agents can reallocate resources to make each member of the coalition better off, thereby signaling that the initial allocation is not in the core.
Explain the significance of aggregate endowment in an exchange economy.
Explain the significance of aggregate endowment in an exchange economy.
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In the context of the given exercise, what does the Edgeworth box illustrate regarding allocations?
In the context of the given exercise, what does the Edgeworth box illustrate regarding allocations?
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What is the role of price optimization in achieving equilibrium in an economy with multiple agents?
What is the role of price optimization in achieving equilibrium in an economy with multiple agents?
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How does the identical utility function assumption simplify the analysis of an exchange economy?
How does the identical utility function assumption simplify the analysis of an exchange economy?
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What would indicate that a specific allocation is not in the core of the economy?
What would indicate that a specific allocation is not in the core of the economy?
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What is the core in the context of an exchange economy?
What is the core in the context of an exchange economy?
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How is the contract curve related to the core in an Edgeworth box?
How is the contract curve related to the core in an Edgeworth box?
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Explain the significance of the Walrasian equilibrium prices in this economic context.
Explain the significance of the Walrasian equilibrium prices in this economic context.
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What determines the feasibility of an allocation in this exchange economy?
What determines the feasibility of an allocation in this exchange economy?
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What indicates that an allocation is no longer in the core when doubling the agents?
What indicates that an allocation is no longer in the core when doubling the agents?
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How do identical agents affect economic equilibrium in this scenario?
How do identical agents affect economic equilibrium in this scenario?
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Define utility functions in the context of economic agents.
Define utility functions in the context of economic agents.
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What is the relationship between contingent commodities and core allocations?
What is the relationship between contingent commodities and core allocations?
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How does price optimization relate to agent behavior in an economy?
How does price optimization relate to agent behavior in an economy?
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Why is it important to assess the relationship between agents' indifference curves when analyzing trade?
Why is it important to assess the relationship between agents' indifference curves when analyzing trade?
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What is the significance of surplus utility when considering allocations among economic agents?
What is the significance of surplus utility when considering allocations among economic agents?
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How can the aggregate endowment be determined for multiple agents?
How can the aggregate endowment be determined for multiple agents?
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What role does price optimization play in consumer decision-making?
What role does price optimization play in consumer decision-making?
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How does the utility function affect an agent's preference for consumption bundles?
How does the utility function affect an agent's preference for consumption bundles?
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Explain the concept of a blocking coalition in the context of economic trade.
Explain the concept of a blocking coalition in the context of economic trade.
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In terms of contingent commodities, why is the allocation between consumers significant?
In terms of contingent commodities, why is the allocation between consumers significant?
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What results when agents 2 and 4 offer part of their consumption to agent 3?
What results when agents 2 and 4 offer part of their consumption to agent 3?
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How is the concept of individual rationality reflected in the allocation among agents?
How is the concept of individual rationality reflected in the allocation among agents?
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Why might economic agents prefer to trade rather than consume their initial endowments?
Why might economic agents prefer to trade rather than consume their initial endowments?
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In what ways can utility functions be used to evaluate the welfare of agents?
In what ways can utility functions be used to evaluate the welfare of agents?
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How does agent B's demand remain unchanged despite changes in agent A's demand?
How does agent B's demand remain unchanged despite changes in agent A's demand?
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What does the equation xA_A + xB = 1 imply about market clearing conditions?
What does the equation xA_A + xB = 1 imply about market clearing conditions?
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In the context of price optimization, what is the significance of finding that pA = 1 is a solution?
In the context of price optimization, what is the significance of finding that pA = 1 is a solution?
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How do differing beliefs between agents A and B lead to incomplete insurance?
How do differing beliefs between agents A and B lead to incomplete insurance?
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What role do utility functions play in the demand equations for agents A and B?
What role do utility functions play in the demand equations for agents A and B?
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What utility function is used for the consumers in the economy with storage?
What utility function is used for the consumers in the economy with storage?
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In the case where consumers cannot trade, how much does consumer 2 consume in each period?
In the case where consumers cannot trade, how much does consumer 2 consume in each period?
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What is the total endowment available in the economy?
What is the total endowment available in the economy?
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When consumer 1 can trade, what is the impact on his storage decisions?
When consumer 1 can trade, what is the impact on his storage decisions?
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How does the introduction of storage costs ($\delta$) affect consumer 1's consumption choices when trading is allowed?
How does the introduction of storage costs ($\delta$) affect consumer 1's consumption choices when trading is allowed?
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Define the term 'Walrasian equilibrium prices' in the context of this economy.
Define the term 'Walrasian equilibrium prices' in the context of this economy.
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What does the Lagrangian formulation help determine in the maximization problem for consumer 1?
What does the Lagrangian formulation help determine in the maximization problem for consumer 1?
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How does consumer 1's utility compare when storage is costly versus when it is not, assuming they can trade?
How does consumer 1's utility compare when storage is costly versus when it is not, assuming they can trade?
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What condition must hold for consumer 1 to prefer to trade rather than consume his entire endowment?
What condition must hold for consumer 1 to prefer to trade rather than consume his entire endowment?
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What can the marginal products derived from the first-order conditions indicate about resource allocation between the two consumers?
What can the marginal products derived from the first-order conditions indicate about resource allocation between the two consumers?
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Consumer 2 consumes a total of 9 units of the good in both periods when trade is not allowed.
Consumer 2 consumes a total of 9 units of the good in both periods when trade is not allowed.
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Consumer 1's utility function is defined as $u(x_1, x_2) = x_1 + x_2$.
Consumer 1's utility function is defined as $u(x_1, x_2) = x_1 + x_2$.
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When storage is costly, the optimal storage decision for consumer 1 does not depend on the value of $eta$.
When storage is costly, the optimal storage decision for consumer 1 does not depend on the value of $eta$.
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The first-order condition derived from the Lagrangian for consumer 1 includes a constraint that $x_2$ must be greater than or equal to 20.
The first-order condition derived from the Lagrangian for consumer 1 includes a constraint that $x_2$ must be greater than or equal to 20.
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The total endowment of the good in this economy is 20 units in total.
The total endowment of the good in this economy is 20 units in total.
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Walrasian equilibrium prices are achieved only when consumers are not allowed to trade.
Walrasian equilibrium prices are achieved only when consumers are not allowed to trade.
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Consumer 1 is better off when storage is allowed but costly compared to when no trade occurs.
Consumer 1 is better off when storage is allowed but costly compared to when no trade occurs.
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Consumer 1 stores 9 units of a good while receiving a utility of 100.
Consumer 1 stores 9 units of a good while receiving a utility of 100.
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If p1 < p2, the firm would make zero profits.
If p1 < p2, the firm would make zero profits.
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The firm optimally chooses y = (0, 0) when p1 > p2.
The firm optimally chooses y = (0, 0) when p1 > p2.
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For any given allocation, m1 + m2 equals 40p1 when there is a contradiction in prices.
For any given allocation, m1 + m2 equals 40p1 when there is a contradiction in prices.
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The first-order conditions for consumer optimization can be expressed as x2i = λp1 and x1i = λp2.
The first-order conditions for consumer optimization can be expressed as x2i = λp1 and x1i = λp2.
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With equilibrium price conditions, p2 x2i equals p1 x1i.
With equilibrium price conditions, p2 x2i equals p1 x1i.
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Feasibility of the equilibrium allocation is ensured when y = (0, 0).
Feasibility of the equilibrium allocation is ensured when y = (0, 0).
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In equilibrium, p1 must equal 2p2 to satisfy all conditions.
In equilibrium, p1 must equal 2p2 to satisfy all conditions.
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X1i = 1 and x2i = 2 indicate a possible production scenario.
X1i = 1 and x2i = 2 indicate a possible production scenario.
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The equilibrium allocation exists only if $δ \geq 12$.
The equilibrium allocation exists only if $δ \geq 12$.
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Agent A receives happiness of 0 if Argentina wins.
Agent A receives happiness of 0 if Argentina wins.
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Agent B believes that Argentina is more likely to win if $πA = 3/4$ and $πB = 1/4$.
Agent B believes that Argentina is more likely to win if $πA = 3/4$ and $πB = 1/4$.
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If both agents agree that Brazil is more likely to win with $πA = πB = 1/4$, the utility of Agent A would be higher than that of Agent B when betting.
If both agents agree that Brazil is more likely to win with $πA = πB = 1/4$, the utility of Agent A would be higher than that of Agent B when betting.
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The utility of agent A is derived from the expression $h^2$.
The utility of agent A is derived from the expression $h^2$.
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The equation $x21 + x22 = ω12 + ω22 + y2$ is part of the feasibility requirement for the economy.
The equation $x21 + x22 = ω12 + ω22 + y2$ is part of the feasibility requirement for the economy.
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The proposed happiness that Agent A wagers for Agent B is a function of the outcome of the World Cup.
The proposed happiness that Agent A wagers for Agent B is a function of the outcome of the World Cup.
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In the context of the Edgeworth box, an optimistic agent always prefers to bet higher amounts on their expected outcome.
In the context of the Edgeworth box, an optimistic agent always prefers to bet higher amounts on their expected outcome.
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The utility of consumer 1 in autarky is represented as $\frac{(1 + 19δ)^2}{4δ}$.
The utility of consumer 1 in autarky is represented as $\frac{(1 + 19δ)^2}{4δ}$.
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The values of $a$ and $b$ in the laundry trade are based on the mutual preferences for happiness between agents A and B.
The values of $a$ and $b$ in the laundry trade are based on the mutual preferences for happiness between agents A and B.
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The statement 'aggregate endowment is zero' indicates aggregate uncertainty.
The statement 'aggregate endowment is zero' indicates aggregate uncertainty.
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If the total endowment across states is constant, then there is no aggregate uncertainty.
If the total endowment across states is constant, then there is no aggregate uncertainty.
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A utility function without the parameter $ ext{Π}$ implies that the agents only care about commodity A.
A utility function without the parameter $ ext{Π}$ implies that the agents only care about commodity A.
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The maximum utility of an agent occurs when the budget constraint is breached.
The maximum utility of an agent occurs when the budget constraint is breached.
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Setting the price of commodity B equal to 1 simplifies the price optimization problem for agents.
Setting the price of commodity B equal to 1 simplifies the price optimization problem for agents.
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The utility functions for agents A and B are different due to differing initial endowments.
The utility functions for agents A and B are different due to differing initial endowments.
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The aggregate endowment affects individual consumption decisions regardless of prices.
The aggregate endowment affects individual consumption decisions regardless of prices.
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If the price of commodity A increases, it will lead to an increase in the quantity of commodity B demanded, all else being equal.
If the price of commodity A increases, it will lead to an increase in the quantity of commodity B demanded, all else being equal.
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In the given economic model, agents can guarantee their utility without trading.
In the given economic model, agents can guarantee their utility without trading.
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If the commodity endowments of two agents are equal, their utility functions must also provide equal utilities.
If the commodity endowments of two agents are equal, their utility functions must also provide equal utilities.
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In this economic model, the relationship between the variables suggests that $mA = pA$ and $mB = 1$ implies a direct correlation between prices and endowments.
In this economic model, the relationship between the variables suggests that $mA = pA$ and $mB = 1$ implies a direct correlation between prices and endowments.
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The formula $xA_i = rac{mA}{pA + 1 - Π imes Πi} imes (pA)^2$ accurately calculates the consumption of agent A based on price optimization.
The formula $xA_i = rac{mA}{pA + 1 - Π imes Πi} imes (pA)^2$ accurately calculates the consumption of agent A based on price optimization.
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The expressions shown suggest that in equilibrium, $ΠA$ and $ΠB$ must both equal 4 for the allocations to be valid.
The expressions shown suggest that in equilibrium, $ΠA$ and $ΠB$ must both equal 4 for the allocations to be valid.
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The total endowment of the economy is represented as 20 units, which is consistent across all calculations involving agent consumption.
The total endowment of the economy is represented as 20 units, which is consistent across all calculations involving agent consumption.
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Agent B's consumption behavior is indicated to be independent of changes made by agent A in the presented equations.
Agent B's consumption behavior is indicated to be independent of changes made by agent A in the presented equations.
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The steady state resource constraint can be expressed as kt+1 = (1 − δ)kt + f(kt, 1) − ______
The steady state resource constraint can be expressed as kt+1 = (1 − δ)kt + f(kt, 1) − ______
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In the steady state, the equation c̄ = k̄ ______ − δk̄ describes the relationship between consumption and capital.
In the steady state, the equation c̄ = k̄ ______ − δk̄ describes the relationship between consumption and capital.
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The modified-golden-rule capital stock is characterized by maximizing long-run ______.
The modified-golden-rule capital stock is characterized by maximizing long-run ______.
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The first steady state equation simplifies to 1 = β(1 + αk̄ ______ − δ).
The first steady state equation simplifies to 1 = β(1 + αk̄ ______ − δ).
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Nullclines in the steady state are represented graphically with k on the ______ axis and c on the vertical axis.
Nullclines in the steady state are represented graphically with k on the ______ axis and c on the vertical axis.
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The steady state Euler equation can be expressed as u(ct) = β(1 + fk(kt+1, 1) − ______)u′(ct+1)
The steady state Euler equation can be expressed as u(ct) = β(1 + fk(kt+1, 1) − ______)u′(ct+1)
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In per capita terms, the production function is given by f(kt, 1) = k̄______.
In per capita terms, the production function is given by f(kt, 1) = k̄______.
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The evolution of capital in the economy is influenced by the rate of ______ and the output produced.
The evolution of capital in the economy is influenced by the rate of ______ and the output produced.
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The steady state is represented when kt+1 equals ______.
The steady state is represented when kt+1 equals ______.
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In the North-east quadrant of the phase diagram, both kt and ct are greater than their steady state values k∗ and c∗, which indicates ______ growth.
In the North-east quadrant of the phase diagram, both kt and ct are greater than their steady state values k∗ and c∗, which indicates ______ growth.
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The saddle path represents how the economy converges to the ______ state.
The saddle path represents how the economy converges to the ______ state.
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In the context of capital accumulation, a shock leading to the destruction of capital stock will lower ______.
In the context of capital accumulation, a shock leading to the destruction of capital stock will lower ______.
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The nullclines in the phase diagram are defined by the values k∗ and c∗ which tell us where ______ dynamics balance.
The nullclines in the phase diagram are defined by the values k∗ and c∗ which tell us where ______ dynamics balance.
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Consumption c0 is chosen such that the bundle {k0, c0} lies on the ______ path.
Consumption c0 is chosen such that the bundle {k0, c0} lies on the ______ path.
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If kt < k∗ and ct < c∗, it indicates that the economy is in a state of ______.
If kt < k∗ and ct < c∗, it indicates that the economy is in a state of ______.
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To calculate the adjustment path following a shock, one must consider how kt+1, ct, wt, and Rt will ______.
To calculate the adjustment path following a shock, one must consider how kt+1, ct, wt, and Rt will ______.
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The transversality condition is key to determining the ______ path in capital accumulation models.
The transversality condition is key to determining the ______ path in capital accumulation models.
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In steady state, the system can continue without ______ change.
In steady state, the system can continue without ______ change.
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The steady state wage depends positively on a: ______
The steady state wage depends positively on a: ______
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The dynamics of capital and consumption are illustrated through the use of ______ in economic models.
The dynamics of capital and consumption are illustrated through the use of ______ in economic models.
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In the context of capital accumulation, the ______ indicates the optimal level of capital that maximizes consumption in the long run.
In the context of capital accumulation, the ______ indicates the optimal level of capital that maximizes consumption in the long run.
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Steady state consumption is influenced by the rate of ______ and the dynamics of the economy.
Steady state consumption is influenced by the rate of ______ and the dynamics of the economy.
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The initial nullclines and saddle paths in a graphical analysis are typically represented in ______.
The initial nullclines and saddle paths in a graphical analysis are typically represented in ______.
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In the context of capital accumulation dynamics, the equation related to the resource constraint is given by kt+1 = kt (1 + rt − ______) + wt − ct.
In the context of capital accumulation dynamics, the equation related to the resource constraint is given by kt+1 = kt (1 + rt − ______) + wt − ct.
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The condition that defines the steady state capital is when kt+1 = ______.
The condition that defines the steady state capital is when kt+1 = ______.
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The golden rule capital stock maximizes steady state ______.
The golden rule capital stock maximizes steady state ______.
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Steady state consumption is directly influenced by the level of ______.
Steady state consumption is directly influenced by the level of ______.
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In nullclines analysis, the intersection points of the ______ define the steady states of the system.
In nullclines analysis, the intersection points of the ______ define the steady states of the system.
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The equation u′(ct) = β(1 + rt+1 − ______)u′(ct+1) is part of the core equation in the economic dynamics.
The equation u′(ct) = β(1 + rt+1 − ______)u′(ct+1) is part of the core equation in the economic dynamics.
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The resource constraint of the economy includes the term f(kt, ______) to represent production.
The resource constraint of the economy includes the term f(kt, ______) to represent production.
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The transversality condition is important for ensuring that initial capital choices lead to a ______ trajectory.
The transversality condition is important for ensuring that initial capital choices lead to a ______ trajectory.
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In the Ramsey model, the representative agent aims to maximize lifetime ______.
In the Ramsey model, the representative agent aims to maximize lifetime ______.
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To find the steady state consumption, one needs to consider the relationship between capital, ______, and output.
To find the steady state consumption, one needs to consider the relationship between capital, ______, and output.
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The steady state consumption falls short of consumption at the modified-golden-rule capital stock due to the consumer not maximizing lifetime ______.
The steady state consumption falls short of consumption at the modified-golden-rule capital stock due to the consumer not maximizing lifetime ______.
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In the Ramsey model, the dynamics of consumption and capital can be studied through the ______ analysis.
In the Ramsey model, the dynamics of consumption and capital can be studied through the ______ analysis.
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The trajectory of capital over time is often represented using a ______ path in phase diagrams.
The trajectory of capital over time is often represented using a ______ path in phase diagrams.
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The resource constraint represents the curve for which ______ stays constant.
The resource constraint represents the curve for which ______ stays constant.
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Optimality conditions derived from the Euler equation define levels of capital for which consumption is ______.
Optimality conditions derived from the Euler equation define levels of capital for which consumption is ______.
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Steady state capital is ideally at the modified-golden-rule level where the marginal utility of consumption is ______.
Steady state capital is ideally at the modified-golden-rule level where the marginal utility of consumption is ______.
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When analyzing capital dynamics, we often look at the relationship between current consumption and ______ consumption.
When analyzing capital dynamics, we often look at the relationship between current consumption and ______ consumption.
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The steady state occurs when the accumulation of ______ is in equilibrium with the depreciating stock.
The steady state occurs when the accumulation of ______ is in equilibrium with the depreciating stock.
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Higher future consumption can result from deciding to invest more capital today rather than increasing current ______.
Higher future consumption can result from deciding to invest more capital today rather than increasing current ______.
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The ______ condition indicates when resources are allocated optimally in terms of capital and consumption.
The ______ condition indicates when resources are allocated optimally in terms of capital and consumption.
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Study Notes
Problem Set 3 Solutions
-
Exercise 4.1: Economy with Storage for one Agent
- Examines an economy with two consumers, a single good, and two time periods.
- Consumers possess intertemporal utility functions (u(x1, x2) = x1x2) and endowments (w₁ = (19,1) & w2 = (1,9)).
- Consumer 1 can store the good, transforming period 1 units into period 2 units.
-
Part 1: Consumers cannot trade.
- Calculates individual consumption levels.
- Assesses consumer well-being.
- Determines the amount of storage.
-
Part 2: Consumers can trade.
- Calculates Walrasian equilibrium prices.
- Determines the amount of storage.
- Assesses consumer well-being.
-
Part 3: Storage is costly.
- Each stored unit recovers at a reduced rate (d) in the second period.
- Determines optimal choices if consumers cannot trade.
- Evaluates the well-being of consumer 1.
-
Part 4: Storage is costly, but consumers can trade.
- Calculates equilibrium prices.
- Identifies when storage occurs.
- Determines when consumer 1 benefits from trade.
Additional Information
- Mathematical notation: Includes mathematical equations showing calculations of consumer utility, equilibrium prices, and storage.
- Agent 1's optimization: Shows Agent 1's maximization problem with storage constraints & cost considerations.
- Feasibility: The model considers situations where storage doesn't occur or is less than it would be in a non-costly model.
- Consumer 2: Consumer 2's choice/optimization is simpler as they have no storage option.
- Equilibrium prices: The role of equilibrium prices in determining storage behavior.
- Part 2 (continued): Deals with the firm's production side and the impact of prices on storage.
- Part 3 (continued): The impact of storage costs on consumer choices.
Other Exercises
- The document also contains information on further exercises (e.g., exercise 4.2 on Argentina and Brazil) related to similar macroeconomic situations concerning consumption over time and with uncertainty.
- Detailed equilibrium conditions and explanations of the core are presented.
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Description
This quiz focuses on Exercise 4.1, which analyzes an economy with storage for one agent over two time periods. It covers consumer utility functions, individual consumption levels, and the implications of trade and storage costs on consumer well-being. Each part of the problem set addresses trade scenarios and the impact of storage choices on optimal decision-making.
