3.1 The Production Function

• A production function illustrates the relationship between the quantity of inputs a firm uses and the maximum quantity of output it can produce.
• Steps to define a production function

  1️⃣ Identify inputs

  2️⃣ Identify outputs

  3️⃣ Express the relationship mathematically
• Inputs in a production function include labor, capital, and raw materials
• What happens to fixed inputs when production increases?

  They remain constant
• Variable inputs decrease when output decreases.
• What is an example of a fixed input in a bakery?

  Oven size
• Variable inputs change with the level of production
• Fixed inputs do not change with output levels.
• Inputs in a production function include labor, capital, and raw materials.
• Inputs in a production function are resources like labor, capital, and raw materials.
• Outputs in a production function are finished goods or services.
• Fixed inputs do not change with the level of production.
• Match the type of input with its definition:

  Fixed Inputs ↔️ Resources that do not change with output

  Variable Inputs ↔️ Resources that change with output
• The short-run production function assumes at least one input is fixed.
• The short-run production function illustrates the relationship between labor and capital when capital is fixed.
• What are fixed inputs in production theory?

  Resources that do not change
• Fixed inputs remain constant regardless of production levels
• Give an example of a fixed input in a bakery.

  Oven size
• Variable inputs change with output levels.
• Match the input type with its definition:

  Fixed Inputs ↔️ Resources that do not change with output

  Variable Inputs ↔️ Resources that change with output
• What is the formula for Average Product (AP)?

  $AP =$$\frac{TP}{Input}$
• Marginal Product (MP) is the additional output gained from adding one more unit of input
• The law of diminishing returns states that output increases indefinitely with more variable inputs.

  False
• Explain the law of diminishing returns using a farming example.

  Adding more farmers reduces marginal yield
• In a bakery example, what is a fixed input?

  The size of the oven
• Fixed inputs remain constant even when output decreases
• What are three examples of variable inputs?

  Labor, raw materials, energy
• Steps for understanding the short-run production function

  1️⃣ Define fixed inputs

  2️⃣ Define variable inputs

  3️⃣ Identify labor and capital

  4️⃣ Analyze the relationship between labor and capital
• Fixed inputs do not change with output levels in the short-run production function.
• In the short-run production function $Q =$$f(L, K)$, capital is assumed to be fixed
• What does the variable $Q$ represent in the short-run production function?


  Quantity of bread
• Average product (AP) measures output per unit of input.
• What is the formula for marginal product (MP)?

  $MP =$$\frac{\Delta TP}{\Delta Input}$
• Match the production metric with its definition:

  Total Product (TP) ↔️ Total quantity of output

  Average Product (AP) ↔️ Output per unit of input

  Marginal Product (MP) ↔️ Additional output from one more input unit
• The law of diminishing returns states that the marginal product of variable inputs eventually decreases
• The law of diminishing returns applies when at least one input is fixed.
• What happens to the marginal product of labor as more bakers are added to a fixed-size oven?

  It decreases
• Average product (AP) is calculated as \frac{TP}{Input}</latex>
• If 5 bakers produce 100 loaves, the average product is 20 loaves per baker.
• The marginal product of input is calculated using the formula $MP =$$\frac{\Delta TP}{\Delta Input}$