Microeconomics: Consumer Theory and Production Theory
10 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What role does a sensor play in feedback control?

  • It compares the desired output to the actual output.
  • It measures the value and feeds it back into the system. (correct)
  • It changes the desired output value.
  • It generates the system's output value.

    • Which factor significantly influences a system’s response to a step input?

  • The dominant pole of the system. (correct)
  • The type of sensor used.
  • The temperature of the environment.
  • The initial system output value.

    • What happens if a system’s dominant pole is complex?

  • The system will approach the steady state smoothly.
  • The system response will be immediate.
  • The system will oscillate before stabilizing. (correct)
  • The system will not reach a steady state.

    • How does a system with a real dominant pole behave?

    <p>It smoothly approaches the steady state, taking longer than a complex system.</p> Signup and view all the answers

    What is the significance of feedback gain in a system?

    <p>It can significantly affect the system’s behavior.</p> Signup and view all the answers

    To what does the gain 'K' refer in feedback control?

    <p>The factor used to determine the system output.</p> Signup and view all the answers

    How does a system typically respond to a step input?

    <p>It may overshoot before settling at a steady-state value.</p> Signup and view all the answers

    What determines the system’s ability to respond to a step input?

    <p>The difference between actual and desired values.</p> Signup and view all the answers

    Under what condition does the system's response indicate an increasing behavior?

    <p>When $f(x_1) &gt; f(x_2)$.</p> Signup and view all the answers

    Where are a system's poles and zeros typically mapped to determine responsiveness?

    <p>On a poles and zeros map.</p> Signup and view all the answers

    Study Notes

    Production Theory

    • Production theory is the opposite of consumer choice theory.

    Consumer Theory

    • The objective function is to maximize utility (Uc) subject to a budget constraint.
    • The utility function is explained by an indifference curve.
    • The marginal rate of substitution (MRS) is the rate at which one good is substituted for another while keeping the level of utility constant.

    Theory of a Firm

    • The objective is to maximize profit (π) by finding the optimal output (q) given the production function q = f(L, K).
    • The production function is explained by isoquants.
    • The marginal rate of technical substitution (MRTS) is the rate at which one input is substituted for another while keeping the output constant.

    Cost Curves

    • Total cost (TC) is the sum of fixed cost (FC) and variable cost.
    • The variable cost is the total expenditure on labor (wL) and capital (Kr).
    • The cost curves are derived from the production function and the cost of inputs.

    Revenue, Variable, and Average Cost

    • Revenue is the total amount of money earned by a business from selling its goods or services.
    • Marginal revenue is the additional revenue earned by selling one more unit of the good or service.

    Aggregate

    • The aggregate is a measure of the total output of a firm or industry.
    • It is affected by the level of inputs and the production function.

    Economic Concepts

    • Profit-maximizing output is the level of output where the marginal cost of production equals the marginal revenue.
    • Law of diminishing marginal product: the marginal product of an input decreases as the input increases.
    • Technical efficiency: the optimal combination of inputs to produce a given output.

    Production Function

    • A production function is a mathematical function that describes the relationship between inputs and outputs.
    • The properties of a production function include:
      • It is never empty.
      • It is increasing in inputs (f'(x) > 0).
      • It is universally hyperexponential.

    Exercise

    • The exercise is to find the rate of change of output when an additional unit of labor is employed, given a production function.
    • The answer is found by taking the derivative of the production function with respect to the input.

    Properties of Production Functions

    • If the production function is strictly increasing, then the marginal product (MP) is positive.
    • If the production function is additively depreciable, then the marginal product is negative.

    Demand and Supply

    • Demand is the quantified product that customers want and are ready to buy at a given price.
    • Supply is the quantified product that producers want and are ready to sell at a given price.
    • The assumptions of demand and supply analysis include:
      • The assumption that everything else remains the same.
      • The demand and supply curves can be represented by a shift in the curve.

    Key Concepts

    • Demand schedule: a table showing the quantity demanded at different prices.
    • Demand curve: a graphical representation of the demand schedule.
    • Supply schedule: a table showing the quantity supplied at different prices.
    • Supply curve: a graphical representation of the supply schedule.
    • Market equilibrium: the point at which the demand and supply curves intersect.
    • Consumer and producer surplus: the difference between the willingness to pay and the market price, and the difference between the market price and the willingness to accept.

    Mathematical Equations

    • The equation for quantity demanded is Qd = 20 - P/2, and for quantity supplied is Qs = P/2 - 5.
    • The equilibrium price and quantity are found by solving the equation Qd = Qs.

    Isoquants and MRTS

    • Isoquants are curves that show the alternative combinations of inputs that can be used to produce a given level of output.
    • The marginal rate of technical substitution (MRTS) is the rate at which one input is substituted for another while keeping the output constant.
    • The MRTS is calculated as the ratio of the change in the input on the y-axis to the change in the input on the x-axis.

    Properties of Isoquants

    • Isoquants are negatively sloped.
    • Isoquants cannot cross.
    • Isoquants are convex to the origin.
    • The higher the isoquant, the higher the output on the isoquant curve.

    Feedback Control

    • Feedback control is a system that uses output equations to invent its own behavior.
    • The system responds to a step input by adjusting its output to reduce the difference between the actual and desired values.

    The System Response

    • The system's response to a step input is determined by its dominant pole.
    • If the pole is complex, the system will oscillate before stabilizing.
    • If the pole is real, the system will smoothly approach the steady-state value.

    The Feedback Gain

    • The feedback gain is a critical factor in the behavior of a system.
    • The gain can be changed in various places.

    The System's Response to a Step Input

    • The system's response to a step input is affected by the output change that occurs because of the step input.
    • The system's ability to respond is determined by the location of the system's poles on the poles and zeros map.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Test your understanding of consumer theory and production theory, including objective functions, utility functions, and profit maximization.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser