General Equilibrium - Exchange Economy
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Questions and Answers

What does general equilibrium refer to in the context of an exchange economy?

  • A single consumer's optimal allocation of goods
  • A scenario with limited goods and consumers
  • The situation where all markets are in equilibrium simultaneously (correct)
  • An economy where resources are not efficiently allocated

    • Which of the following statements correctly describes the setup of the exchange economy?

  • Each consumer can generate additional income from external sources
  • Both consumers have initial endowments of each good (correct)
  • There are three consumers and one good
  • Prices of goods are fixed and do not affect demand

    • In the budget constraint equation for consumer A, which of the following correctly represents their total income?

  • $I_A = px e_A + py e_A$ (correct)
  • $I_A = px e_A + py e_B$
  • $I_A = px e_A + py e_A + pc e_C$
  • $I_A = px e_B + py e_B$

    • Which of the following factors directly influences consumer demand within the budget constraints?

    <p>Prices of goods and consumer income</p> Signup and view all the answers

    What is the primary role of consumers A and B in the exchange economy as outlined?

    <p>To trade their initial endowments to fulfill their needs</p> Signup and view all the answers

    What is necessary for an equilibrium in the economy?

    <p>Optimization and market clearing are required.</p> Signup and view all the answers

    What does the term 'market clearing' signify in a general equilibrium framework?

    <p>Equating supply and demand in multiple markets simultaneously.</p> Signup and view all the answers

    According to Walras's Law, which of the following statements is correct?

    <p>If all but one market clears, the final market will clear as well.</p> Signup and view all the answers

    What do we need to find to define an equilibrium in a market?

    <p>Allocations of goods and prices for each good.</p> Signup and view all the answers

    How can equilibrium prices and allocations be practically solved?

    <p>By finding Marshallian demands and applying market clearing conditions.</p> Signup and view all the answers

    What is the utility function used for both consumers?

    <p>U(x, y) = x^{1/2}y^{1/2}</p> Signup and view all the answers

    What is the Marshallian demand for good x for consumer A?

    <p>$\frac{1}{2} \frac{25px + 75py}{px}$</p> Signup and view all the answers

    How is the income for consumer A calculated?

    <p>$I_A = 25px + 75py$</p> Signup and view all the answers

    What condition must be satisfied for the market to clear for good x?

    <p>$x_A + x_B = e_A + e_B$</p> Signup and view all the answers

    What is the equilibrium allocation of good x for both consumers?

    <p>$x_A = 50, x_B = 50$</p> Signup and view all the answers

    What does the equality of the prices of the two goods imply?

    <p>The market is in equilibrium.</p> Signup and view all the answers

    Which of the following represents the correct expression for Marshallian demand of good y for consumer B?

    <p>$\frac{1}{2} \frac{75px + 25py}{py}$</p> Signup and view all the answers

    If the prices of both goods are the same, what can be inferred about the consumer's preferences?

    <p>Consumers are indifferent between the two goods.</p> Signup and view all the answers

    What does the result of the market clearing prices indicate about relative prices?

    <p>It shows that both goods must have the same price.</p> Signup and view all the answers

    What is the total endowment of good x across both consumers?

    <p>100</p> Signup and view all the answers

    Study Notes

    General Equilibrium - Exchange Economy

    • General equilibrium describes a situation where all markets are in equilibrium simultaneously.
    • Models can become complex, so a simplified exchange economy model is built from basic assumptions.

    Concepts Covered

    • Exchange Economy
    • Walrasian General Equilibrium
    • Pareto Efficiency and the Welfare Theorems

    Exchange Economy Setup

    • Two Consumers: A and B
    • Two Goods: x and y
    • Endowments: Each consumer starts with a given amount of each good (eAx, eAy, eBx, eBy). Total endowment is Ex and Ey
    • Trade: Consumers can buy or sell goods at prices px and py.
    • Budget Constraints: Consumers' income is derived from selling their endowments. IA = pxeAx + pyeAy and IB= pxeBx + pyeBy

    Walrasian General Equilibrium

    • Market Clearing: Supply and demand must be equal across all markets
    • Theorem: Walras' Law guarantees that if all but one market clears, the final market will as well.
    • Equilibrium Components: An equilibrium requires an allocation of goods for each consumer (xA, yA, xB, yB) and prices (px, py) which satisfy these two conditions:
      • Allocation maximizes each consumer's utility given their budget constraints.
      • All markets clear. Mathematically, (xA + xB) = Ex and (yA + yB) = Ey.

    Pareto Efficiency

    • Definition: An allocation is Pareto efficient if there is no other feasible allocation where at least one person is better off and no one is worse off.
    • MRS: Allocations with different Marginal Rates of Substitution (MRS) suggest potential gains from trade. Consumers may have different preferences over goods, generating possible improvements for both parties.

    Welfare Theorems

    • First Welfare Theorem: Any Walrasian equilibrium is Pareto efficient.
    • Second Welfare Theorem: Any Pareto efficient allocation can potentially be achieved as a Walrasian equilibrium with appropriate initial endowments.

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    General Equilibrium - Exchange Economy PDF

    Description

    Explore the foundational concepts of general equilibrium within an exchange economy. This quiz covers key topics such as Walrasian General Equilibrium, Pareto Efficiency, and the Welfare Theorems, including the setup of a two-consumer model. Test your understanding of how consumers interact and trade goods within an equilibrium framework.

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