Budget equation

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Intros
Lessons
  1. Budget Equation Overview:
  2. The Budget Equation
    • All the available options when income is used
    • QxPx+QyPyQ_x P_x + Q_y P_y = I
    • Qx Q_x \, →  \, quantity of x, Qy  Q_y \, →  \, quantity of = y
    • Px P_x \, →  \, price of x, Py  P_y \, →  \, price of = y
    • I I \, →  \, income
  3. Changes to the Budget Equation
    • Increase in the price of good x
    • Decrease in the price of good x
    • Increase in the price of good y
    • Decrease in the price of good y
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Examples
Lessons
  1. Understanding the Changes to the Budget Constraint
    Suppose a consumer can buy two goods, fruits and candy. The price of fruits is $5 each, and the price of candies are $10 each. If the consumer as an income of $50, then find the budget equation and graph it.
    1. Suppose you are interested in two goods, monitors and laptops. The price of monitors is $200 each, and the price of laptops are $600 each. If your total income is $1200, then find the slope and y-intercept of your budget equation.
      1. Suppose a consumer can buy two goods, fruits and candy. The price of fruits is $5 each, the price of candies is $20 each, and the consumer's income is $60. Suppose the income of the consumer increases to $100.
        1. Find and graph the original budget line
        2. Find and graph the new budget line
        3. Is the slope steeper or less steep, or unchanged?
        4. Calculate the slope and y-intercept of the new budget line.
      2. Suppose a consumer can buy two goods, pencils and erasers. The price of pencils is $2 each, the price of erasers is $1 each, and the consumer's income is $6. Suppose the price of erasers increase to $2.
        1. Find and graph the original budget line
        2. Find and graph the new budget line
        3. Is the slope steeper or less steep, or unchanged?
        4. Calculate the slope and y-intercept of the new budget line.
      Topic Notes
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      Recall the budget line from last section. We will look further into what the equation of this line, and changes that could affect the budget equations.


      The Budget Equation

      If all income has been used for the goods, then the budget line is expressed by the linear equation:


      xPx+yPy=IxP_x+yP_y=I

      Where
      x → quantity of good x
      y → quantity of good y
      PxP_x → price of good x
      PyP_y → price of good y
      I → income

      Budget equation

      Note: The slope and y-intercept of the budget equation can be found by putting the equation into the form y = mx + b.


      xPx+yPy=IxP_x+yP_y=I →yPy=−xPx+1 yP_y = -xP_x+1

      →y=−PxPyx+IPy y=- \frac{P_x}{P_y}x+\frac{I}{P_y}

      Thus,
      Slope=−PxPy,y−intercept=IPy Slope= - \frac{P_x}{P_y},y-intercept=\frac{I}{P_y}

      Changes to the Budget Equation


      The budget equation can be changed in 6 basic ways.
      Increase the price of good x: The consumer will buy less of good x, causing the budget line to be steeper.

      Budget equation

      Decrease the price of good x: The consumer will buy more of good x, causing the budget line to be less steep.

      Decrease the price of good

      Increase the price of good y: The consumer will buy less of good y, causing the budget line to be less steep.

      Increase the price of good y

      Decrease the price of good y: The consumer will buy more of good y, causing the budget line to be steeper.

      Decrease the price of good y

      Increase the Income: The consumer will buy more of both goods, causing the budget line to shift rightward. The slope stays the same.

      Increase the Income

      Decrease the Income: The consumer will buy less of both goods, causing the budget line to shift leftward. The slope stays the same.

      Decrease the Income