General Equilibrium - Production Economy
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Questions and Answers

What does the Production Possibility Frontier (PPF) illustrate?

  • The fixed labor input required for each good's production
  • The set of possible combinations of two goods that can be produced (correct)
  • The relationship between the prices of goods and labor costs
  • The total income generated by consumers in an economy

    • What is a key difference between the production economy and the exchange economy?

  • The firm chooses production amounts based on good prices (correct)
  • The supply of each good is fixed
  • Consumers do not own shares in the firm
  • Firms can produce only one good

    • In a production economy, how is the total income to consumers generated?

  • From selling their labor to the firm
  • Through fixed wages paid by the firm
  • Based on the prices of the goods sold
  • By sharing profits from goods produced (correct)

    • If the firm has a fixed amount of labor, how does it allocate labor between the two goods?

    <p>Using production functions to determine the optimal distribution</p> Signup and view all the answers

    What must hold true for the firm in a production economy with two goods?

    <p>The sum of labor used must equal the total available labor</p> Signup and view all the answers

    What is the formula for y when solving for y in the labor supply equation?

    <p>y = L̄ − x^2</p> Signup and view all the answers

    What does the marginal product of labor (MPL) for good x indicate?

    <p>MPLx decreases as more labor is applied to produce x.</p> Signup and view all the answers

    What characterizes the shape of the production possibilities frontier (PPF)?

    <p>Concave due to increasing opportunity costs.</p> Signup and view all the answers

    If all labor is utilized in producing good y, what is the maximum quantity of y that can be produced?

    <p>10</p> Signup and view all the answers

    What does the Rate of Product Transformation (RPT) represent in the context of a firm’s production?

    <p>The relationship between the marginal costs of producing two goods.</p> Signup and view all the answers

    What effect does increasing the production of good x have on the opportunity cost of production?

    <p>It increases the opportunity cost of producing good y.</p> Signup and view all the answers

    In the equation $L̄ = Lx + Ly = x^2 + y^2$, what does the right-hand side represent?

    <p>The total cost incurred by the firm for producing goods.</p> Signup and view all the answers

    What occurs to the slope of the PPF as $y$ approaches 0 and $x$ approaches 10?

    <p>The slope approaches negative infinity.</p> Signup and view all the answers

    How is the RPT calculated using the marginal costs of the two goods?

    <p>By calculating the ratio of the marginal costs $M C_x$ to $M C_y$.</p> Signup and view all the answers

    What is the relationship between the RPT and the slope of the PPF?

    <p>The RPT matches the negative slope of the PPF.</p> Signup and view all the answers

    What is indicated by a concave production possibility frontier (PPF)?

    <p>Increasing opportunity cost as production of one good increases.</p> Signup and view all the answers

    How does the firm's revenue function for producing two goods relate to profit maximization?

    <p>Revenue is calculated by summing the product of price and quantity for each good.</p> Signup and view all the answers

    What remains constant for a firm operating along the production possibility frontier?

    <p>The amount of labor available or employed.</p> Signup and view all the answers

    What does the term 'specialization of workers' imply in the context of a concave PPF?

    <p>Only certain workers are effective at producing one specific good.</p> Signup and view all the answers

    What is the implication of maximizing profit under the constraint of being on the production possibility frontier?

    <p>Maximizing profit requires an increase in the total revenue collected.</p> Signup and view all the answers

    Study Notes

    General Equilibrium - Production Economy

    • This model extends the general equilibrium model, incorporating production.
    • Concepts covered include the production economy, production possibility frontier (PPF), rate of product transformation (RPT), profit maximization with two goods, and equilibrium.

    The Production Economy

    • The model maintains the basic structure of the exchange economy, but includes key differences:
      • Two goods (x, y)
      • A single firm produces both goods using distinct production technologies, each using a single input: labor (L).
      • Fixed labor supply (L)
      • Firms sell goods at prices (Px, Py).
      • Consumers have identical utility functions, own equal shares of the firm, and receive all profits as total income.

    The Production Possibility Frontier (PPF)

    • The PPF represents all feasible combinations of goods (x, y) producible at full employment of resources.
    • Assuming full labor use, the relationship between x and y can be expressed.
    • An example illustrates this concept using production functions: x = L1/2 and y = L1/2, leading to the equation L = x² + y².
    • Solving for y results in the PPF function: y = (L – x2)1/2 .
    • The PPF (with L = 100) is a curve demonstrating the production trade-off.

    The Rate of Product Transformation (RPT)

    • The RPT is the negative of the PPF's slope, representing the opportunity cost of producing one good in terms of the other.
    • The RPT is equivalent to marginal cost of x over marginal cost of y.

    Profit Maximization with Two Goods

    • Firms aim to maximize profits, considering the constraint posed by the PPF.
    • The revenue from selling goods is price times quantity for each good.
    • Firm's cost is constant along the PPF (fixed labor quantity).
    • Profit maximization translates to maximizing revenue subject to the PPF.

    Equilibrium

    • Equilibrium in this context is achieved when both firms maximize profits and consumers maximize utility.
    • The price ratio (Px/Py) must equal the RPT and the marginal rate of substitution (MRS) of x and y for consumers.
    • This condition ensures equilibrium, with market clearing for both goods.
    • The provided example illustrates the steps to find the equilibrium, using a given example utility function and production functions, with 200 workers available.

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    Description

    Explore the intricacies of the general equilibrium model within a production economy. This quiz covers fundamental concepts such as the production possibility frontier, profit maximization, and the interaction between two goods produced by a single firm. Test your understanding of how equilibrium is achieved in this model.

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