Study notes for Chapter 14: Behind the Supply Curve: Inputs and Costs

Chapter 14: Behind the Supply Curve: Inputs and Costs

The Production Function

• Definition of a Firm: A firm is an organization that produces goods or services for sale.

• Production Process: Production is the process of turning inputs into outputs.

• Production Function: The production function represents the relationship between the quantity of inputs a firm uses and the quantity of output it produces.

• Fixed Input: An input whose quantity is fixed for a period of time and cannot be varied.

• Variable Input: An input whose quantity the firm can vary at any time.

Inputs and Output

• Long Run: The period in which all inputs can be varied.

• Short Run: The period in which at least one input is fixed.

• Total Product Curve: The total product curve shows how the quantity of output depends on the quantity of the variable input for a given quantity of the fixed input.

Production Function and Total Product Curve (1 of 2)

• Marginal Product (MP): The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input.

• Marginal Product of Labor (MPL): Defined as the change in output resulting from a one-unit increase in the amount of labor input, mathematically represented as:
  $ext{MPL} = rac{ riangle Q}{ riangle L}$ where ( riangle Q ) is the change in output and ( riangle L ) is the change in labor.

• Slope of Total Product Curve: MPL equals the slope of the total product curve.

• Observation: As additional workers are hired, the MPL declines and the total product curve flattens (Figure 1).

• Figure 2: Illustrates how MPL depends on the number of workers.

Production Function and Total Product Curve (2 of 2)

• Curve Behavior: The total product curve slopes upward due to increased wheat production with more employees, but flattens due to diminishing returns as more workers are added.

• Diminishing Returns to an Input: An increase in the quantity of that input, holding levels of all other inputs fixed, leads to a reduction in that input's marginal product.

Related Questions

• Deli Fixed Input Example: For a deli, the dining room is likely the fixed input while ingredients like bread and tomatoes are variable inputs.

• Worker Marginal Product Calculation: If one worker makes 14 baskets, two workers make 34 baskets, three make 45 baskets, and four make 50, the highest marginal product is contributed by the first worker.

Total Product, Marginal Product, and Fixed Input

• Impact of Land (Fixed Input): More land allows higher total production per worker, shifting the total product curve and the MPL curve upward.

Pitfalls: What’s a Unit?

• Unit of Labor Definition: The MPL is defined by the increase in output when the quantity of labor is increased by one unit. Consistency in defining what constitutes a unit (e.g., hour, week) is key.

From the Production Function to Cost Curves

• Fixed Cost (FC): A cost that does not depend on the quantity of output produced; related to fixed inputs.

• Variable Cost (VC): A cost that depends on the quantity of output produced; related to variable inputs.

Total Cost Curve

• Total Cost Equation: The total cost of producing a given quantity of output is the sum of fixed and variable costs:
  $TC = FC + VC$

• Total Cost Curve Representation: Shows how total cost varies with output.

Marginal Cost

• Definition of Marginal Cost (MC): The change in total cost generated by one additional unit of output, mathematically defined as:
  $MC = rac{ riangle TC}{ riangle Q}$

Marginal Cost Graphs

• Behavior of the Total Cost Curve: The curve steepens with more output due to diminishing returns, demanding more labor for additional output, hence increasing marginal costs.

Example of Marginal Cost

• Selena's Gourmet Salsas Example: Table providing fixed costs, variable costs, total costs, and marginal costs at various quantities of salsa produced.

Why Is The Marginal Cost Curve Upward Sloping?

• The upward slope of the marginal cost curve is primarily due to diminishing returns. As output increases, the marginal product of the variable input declines, requiring more input for each additional unit of output, leading to higher costs.

Average Cost

• Average Total Cost (ATC): Calculated as the total cost per unit of output, given by:
  $ATC = rac{TC}{Q}$

• Average Fixed Cost (AFC): Calculated as the fixed cost per unit of output, given by:
  $AFC = rac{FC}{Q}$

• Average Variable Cost (AVC): Calculated as the variable cost per unit of output, given by:
  $AVC = rac{VC}{Q}$

Example Question on Average Total Cost

• Given a current production of 4 widgets at $40, a production of a fifth widget (MC $5) results in average total cost calculations indicating changes in average total cost.

Average Costs for Selena’s Gourmet Salsas

• Table showing total cost, average total cost, average fixed cost, and average variable cost for different quantities of salsa.

Average Total Cost Curve for Selena's Gourmet Salsas

• The shape of the average total cost curve is U-shaped, showing minimum average total cost with increasing quantity of output.

Average Total Cost Curve Dynamics

Effects on Average Total Cost:

1. Spreading Effect: Larger output spreads the fixed cost over more units, thus lowering average fixed cost.

2. Diminishing Returns Effect: Larger outputs increase the variable input needed for additional units, thus raising average variable cost.

• At low output levels, the spreading effect predominates; at high levels, diminishing returns effect dominates.

Practical Example of Input Switching

• Coca-Cola's Input Change: Faced with rising sugar costs, Coca-Cola switched from cane sugar (fixed input) to corn sugar (variable input), potentially lowering total costs.

Cost Curve Relationships

• Slope Behavior: Marginal cost increases upward due to diminishing returns while average variable cost rises slower than marginal cost. The marginal cost curve intersects the average total cost curve at its lowest point.

Minimum Average Total Cost

• Minimum-Cost Output Definition: It's the point of lowest average total cost on the U-shaped average total cost curve.

• **Principles at Minimum-Cost Output: **

  1. At the minimum-cost output, ATC equals MC.

  2. When output is below minimum-cost output, MC < ATC and ATC is falling.

  3. When output is above minimum-cost output, MC > ATC and ATC is rising.

The Relationship Between Average Total Cost and Marginal Cost Curves

• The behavior of the marginal cost curve indicates its impact on the average total cost curve: a rising MC leads to rising ATC and vice versa based on MC's position relative to ATC.

Marginal Cost Curve Behavior

Typical Swoosh Shape:

• The marginal cost curve may initially slope downward due to gains from specialization but eventually slopes upward due to diminishing returns.

Short-run Versus Long-run Costs

• In the long run, all inputs are variable, allowing firms to choose fixed costs based on production expectations.

Choosing the Level of Fixed Cost

• There is a trade-off between fixed costs and variable costs at any output level, impacting overall cost management.

The Long-run Average Total Cost Curve

• Represents the relationship between output and average total cost when firms select fixed costs that minimize average total cost for each output level.

Short-run and Long-run Average Total Cost Curves

• Short-run and long-run average total cost curves differ based on the firm's ability to choose fixed costs, impacting optimization of cost at various output levels.

Returns To Scale

• Economies of Scale: When long-run average total cost declines with increased output, indicating increasing returns to scale.

• Diseconomies of Scale: When long-run average total cost increases with increased output, indicating decreasing returns to scale.

• Constant Returns to Scale: Occurs when long-run average total cost remains constant with output increases.