Firm Behavior: Production, Costs, and Supply

Ronald Coase and the Nature of the Firm

• Ronald Coase: An economist born in 1910, awarded the Nobel Prize in 1991 for his studies on transaction costs.

• Core Question: What is a firm?

• Coase's Distinction:

  • In a market economy, transactions involve going to a market and paying a price for goods or services.

  • Within a firm, the price mechanism is absent. Instead, a manager or "entrepreneur coordinator" directs workers to perform tasks without explicit internal pricing for individual actions.

• Quote: "Outside the firm, price movements direct production, which is coordinated through a series of exchange transactions on the market. Within a firm, these market transactions are eliminated and in place of the complicated market structure with exchange transactions is substituted the entrepreneur coordinator who directs production."

• Key Idea: The distinguishing mark of a firm is "the supersession of the price mechanism."

The Production Function

• Definition: In economics, the production function is treated as a "black box" summarizing everything that happens within a firm that is not related to the price mechanism. It abstracts away from internal coordination details to focus on overall input-output relationships for studying prices.

• Inputs: Capital, labor, land.

• Output: The quantity ($ext{Q}$) of goods or services produced.

• Example: With 1 oven (capital) and 3 workers (labor), a firm can produce 12 pizzas per day.

• Goal: To understand how inputs are transformed into outputs, without delving into the specifics of internal firm management.

Marginal Product

• Definition: The extra units of output produced when one additional unit of an input is used, holding all other inputs constant.

• Marginal Product of Labor ($ext{MPL}$): How many extra units of a good can be produced if one extra worker is hired.

• Marginal Product of Capital ($ext{MPK}$): How many extra units of a good can be made if an additional unit of capital (e.g., a new oven) is acquired.

• Significance: Measures the increase in output from an additional unit of input, analogous to marginal utility in consumer theory.

Diminishing Marginal Product (or Returns)

• Concept: While marginal product is generally positive (more inputs lead to more output), the contribution of each additional unit of input will eventually decrease. The first units of an input are typically the most productive.

• Historical Context: David Ricardo (18th/19th century) initially applied this concept to land, arguing that the most fertile land is used first, and subsequent additions of land would be less productive.

• Modern View: With fixed capital (e.g., only two ovens), adding more and more workers will eventually lead to diminishing returns, as workers become less efficient due to overcrowding or limited tools.

Production Function Example & Marginal Product Calculation

• Scenario: Capital is fixed, focusing on the impact of labor.

• Data Table:
  

  Workers	Units Made	Marginal Product (MP)
  0	0	-
  1	50	50
  2	110	60
  3	180	70
  4	240	60
  5	280	40
  6	300	20
  7	308	8
  Marginal Product Calculation: Calculated as the difference in "Units Made" for each additional worker.

  • E.g., for the 2nd worker: $110 - 50 = 60$.

• Plotting Marginal Product:

  • Initially Increasing: From 50 to 70 (due to division of labor/specialization among early workers).

  • Eventually Decreasing: From 70 to 8 (consistent with the law of diminishing marginal returns, as fixed capital becomes a limitation).

• Note: Marginal Product is undefined for zero workers as there's no prior unit to compare against.

Average Product

• Definition: The total number of units produced divided by the number of workers ($ext{AP} = rac{ ext{Total Output}}{ ext{Workers}}$).

• Significance: The simplest and most intuitive measure of productivity per worker.

• Data Table (continued):
  

  Workers	Units Made	Marginal Product (MP)	Average Product (AP)
  0	0	-	-
  1	50	50	50
  2	110	60	55
  3	180	70	60
  4	240	60	60
  5	280	40	56
  6	300	20	50
  7	308	8	44 (approx)
  Plotting Average Product: Typically an inverted U-shape.
  Relationship between Marginal Product (MP) and Average Product (AP):

  • If ext{MP} > ext{AP} , the AP curve is rising (e.g., new grades higher than average pull the average up).

  • If ext{MP} < ext{AP} , the AP curve is falling (e.g., new grades lower than average pull the average down).

  • Intersection: The MP curve always intersects the AP curve at the AP's maximum point. This is because the marginal unit determines whether the average will rise or fall.

• Note: Average Product is undefined for zero workers due to division by zero.

The Cost Function

• Definition: Takes the quantity of units a firm wants to produce as input and returns the associated monetary cost as output.

• Decomposition of Total Cost (TC):

  • Fixed Cost (FC): Costs that do not vary with the quantity of output produced (e.g., rent, lease payments for a factory). These must be paid regardless of whether production occurs.

  • Variable Cost (VC): Costs that vary with the quantity of output produced (e.g., wages for hourly workers, raw materials).

  • $ext{TC} = ext{FC} + ext{VC}$

• Industry Specificity: The distinction between fixed and variable costs can vary significantly between industries.

• Opportunity Cost: In economics, total cost always includes opportunity cost. This means that if a firm is making "zero economic profits", it is still earning enough to cover all explicit costs and the implicit cost of alternative uses for its resources (e.g., the profit the owner could make in another venture). This differs from accounting profits.

• Information Equivalence: The cost function encodes the same information as the production function, just viewed from a different perspective (cost of output versus output from inputs).

Marginal Cost (MC)

• 
  

• Definition: The extra cost incurred to produce one additional unit of output ($ext{MC} = rac{ ext{Change in Total Cost}}{ ext{Change in Quantity}} = rac{ ext{dTC}}{ ext{dQ}}$).

• 
  

• Relationship to Marginal Product: Because of diminishing marginal product, producing more and more units often requires successively more resources (e.g., more workers for a given output), leading to an increasing marginal cost.

• 
  

• Approximation Formula (when quantity doesn't change by 1 unit):
  $ext{MC} = rac{ ext{TC}<em>{ ext{current}} - ext{TC}</em>{ ext{previous}}}{ ext{Q}<em>{ ext{current}} - ext{Q}</em>{ ext{previous}}}$

• 
  

• Cost Function Example (using previous production data + assumptions: fixed cost = $120, worker wage = $240/worker):
  

  Units (Q)	Fixed Cost (FC)	Variable Cost (VC)	Total Cost (TC)	Marginal Cost (MC)
  0	$120	$0	$120	-
  50	$120	$240	$360	$4.80	(($360-$120)/$(50-0))
  110	$120	$480	$600	$4.00	(($600-$360)/$(110-50))
  180	$120	$720	$840	$3.43	(($840-$600)/$(180-110))
  240	$120	$960	$1,080	$4.00	(($1,080-$840)/$(240-180))
  280	$120	$1,200	$1,320	$6.00	(($1,320-$1,080)/$(280-240))
  300	$120	$1,440	$1,560	$12.00	(($1,560-$1,320)/$(300-280))
  308	$120	$1,680	$1,800	$30.00	(($1,800-$1,560)/$(308-300))
  Plotting Marginal Cost: The MC curve is typically U-shaped. It may initially decrease due to efficiency gains (division of labor) but eventually rises steeply due to diminishing marginal returns to inputs.
  Average Cost Curves

  • Average Total Cost (ATC): Total Cost per unit of output ($ext{ATC} = rac{ ext{TC}}{ ext{Q}} = rac{ ext{FC} + ext{VC}}{ ext{Q}} = ext{AFC} + ext{AVC}$).

  • Average Variable Cost (AVC): Variable Cost per unit of output ($ext{AVC} = rac{ ext{VC}}{ ext{Q}}$).

  • Average Fixed Cost (AFC): Fixed Cost per unit of output ($ext{AFC} = rac{ ext{FC}}{ ext{Q}}$). AFC always declines as quantity increases.

  • Plotting Average Cost Curves:

    • Both ATC and AVC curves are typically U-shaped.

    • The MC curve intersects both the AVC and ATC curves at their respective minimum points.

    • Relationship to MC:

      • If ext{MC} < ext{ATC} (or $ext{AVC}$), the average is decreasing.

      • If ext{MC} > ext{ATC} (or $ext{AVC}$), the average is increasing.

  • Efficient Scale: The quantity of output at which Average Total Cost (ATC) reaches its minimum value. Producing at this scale implies the lowest per-unit cost, which is desirable from an efficiency standpoint.

  Profit Maximization

  • Assumption: Price Taker (Competitive Firm): For simplicity, a firm is assumed to be small relative to its market, unable to influence the market price ($ext{P}$) of its product or the wages ($ext{W}$) it pays. This serves as a benchmark for understanding firm behavior.

  • Short Run vs. Long Run:

    • Short Run: A period where at least one input (typically capital) is fixed and cannot be changed. Firms are obligated to pay fixed costs.

    • Long Run: A period where all inputs are variable; firms can adjust all factors of production, including capital, and can enter or exit an industry.

    • The definition of short/long run is industry-specific (e.g., 2 years for a pizza shop vs. many years for an oil rig).

  • Profits ($ext{Π}$): The primary goal of a firm is to maximize profits. $ext{Π} = ext{Total Revenue (TR)} - ext{Total Cost (TC)}$

    • $ext{TR} = ext{Price (P)} imes ext{Quantity (Q)}$

    • Reminder: TC includes opportunity cost.

  Profit Maximization Example

  • 
    

  • Assumed Cost Functions:

    • $ext{TC} = ext{Q}^2 + 100$ (Fixed Cost = $100$)

    • $ext{MC} = 2 ext{Q}$

  • 
    

  • Derived Costs:
    

    Q	TC	MC	ATC ($rac{ ext{TC}}{ ext{Q}}$)
    5	$125	$10	$25
    10	$200	$20	$20
    15	$325	$30	$21.67
    20	$500	$40	$25
    25	$725	$50	$29
    Efficient Scale: The quantity where ATC is minimized (here, $ext{Q} = 10$ at ext{ATC} = $20 ).
    Profit Calculation (assuming Price P = $30):
    Q	TR ($ext{P} imes ext{Q}$)	TC	Π ($ext{TR} - ext{TC}$)
    ---	---	---	---
    5	$150	$125	$25
    10	$300	$200	$100
    15	$450	$325	$125
    20	$600	$500	$100
    25	$750	$725	$25
    Profit-Maximizing Quantity: $ext{Q} = 15$, yielding ext{Π} = $125 . This is found by comparing marginal revenue and marginal cost.
    Marginal Revenue (MR) and the Profit Maximization Rule

    • Marginal Revenue (MR): The extra revenue gained from selling one additional unit of output.

    • For a Competitive Firm: Since the firm is a price taker, it can sell any quantity at the given market price. Therefore, $ext{MR} = ext{Price (P)}$.

    • Profit Maximization Rule (General): A firm maximizes profit by producing the quantity where Marginal Revenue (MR) = Marginal Cost (MC).

    • Profit Maximization Rule (Competitive Firm): Produce where Price (P) = Marginal Cost (MC).

    • Intuition:

      • If P > MC : Producing an additional unit brings in more revenue than its cost, so profit increases ($<br>ightarrow$ produce more).

      • If P < MC : Producing an additional unit costs more than the revenue it brings in, so profit decreases ($<br>ightarrow$ produce less).

      • The optimal point is where $P = MC$. (In the example, at $Q=15$, P=$30 , MC=$30 ).

    • Visualizing Profits on a Graph:

      1. Identify the optimal quantity (Q*) where $ext{P} = ext{MC}$.

      2. Find the Average Total Cost (ATC) at Q*.

      3. The profit rectangle is formed by $( ext{P} - ext{ATC}) imes ext{Q*}$. This area represents the total profit.

    Alternative View: Factor Demand

    • The profit maximization problem can also be viewed from the perspective of how many inputs (e.g., workers) to hire.

    • Condition for Optimal Input (e.g., Labor): $ext{Price (P)} imes ext{Marginal Product of Labor (MPL)} = ext{Wage (W)}$.

      • Left-hand side: Marginal Revenue Product of Labor ($ext{MRP}_ ext{L}$) – the additional revenue generated by hiring one more worker.

      • Right-hand side: Marginal Cost of Labor ($ext{MCL}$) – the wage paid to one more worker.

    • Interpretation: Hire workers as long as the additional revenue they generate exceeds their wage. Stop when $ext{P} imes ext{MPL} = ext{W}$.

    • Connection: This input-side condition is mathematically equivalent to the output-side $ext{P} = ext{MC}$ condition for profit maximization.

    The Firm's Supply Curve

    • The firm's supply curve arises directly from its profit maximization decision for different prices.

    • Long-Run Supply:

      • Firms will only produce if they can make positive economic profits (i.e., revenues cover all costs, including opportunity cost).

      • The firm supplies quantity $ext{Q}$ where $ext{P} = ext{MC}$. However, if ext{P} < ext{Minimum Average Total Cost (ATC)} , the firm will exit the industry and supply zero units.

      • The long-run supply curve is the portion of the MC curve that lies above the minimum point of the ATC curve.

    • Short-Run Supply:

      • In the short run, firms face fixed costs that must be paid regardless of production. They might continue to produce even if making a loss, as long as it covers variable costs.

      • Three Cases for Short-Run Production Decision:

        1. $ext{P} ext{ extgreater} ext{ ATC}$: Firm makes a positive profit. Stays open, produces where $ext{P} = ext{MC}$. (Same as long run)

        2. $ext{ATC} ext{ extgreater} ext{ P} ext{ extge} ext{ AVC}$: Firm makes a negative profit (a loss), but the price covers variable costs and partially contributes to fixed costs. Stays open, produces where $ext{P} = ext{MC}$. This minimizes losses because shutting down would mean losing all fixed costs.

        3. $ext{P} ext{ extless} ext{ AVC}$: The price doesn't even cover variable costs. The firm should shut down immediately to avoid incurring greater losses from production, as it can save on variable costs. Supplies zero units ($ext{Q} = 0$).

      • The short-run supply curve is the portion of the MC curve that lies above the minimum point of the AVC curve.

    Summary of Supply and Demand Models

    • Demand Slope: The demand curve slopes downward primarily due to the principle of diminishing marginal utility (consumers get less additional satisfaction from each extra unit).

    • Supply Slope: The supply curve slopes upward primarily due to the principle of diminishing marginal product (firms face increasing marginal costs as they produce more, which requires higher prices to incentivize production).

    • Movements vs. Shifts:

      • Movement along the curve: Caused by a change in the product's own price.

      • Shift of the curve: Caused by changes in other factors:

        • Supply: Changes in input costs, technology, number of sellers.

        • Demand: Changes in income, tastes, prices of related goods, number of buyers.

    • Foundation: These fundamental microeconomic principles (diminishing marginal utility and product) are crucial for understanding the shapes of the demand and supply curves and form the basis for market equilibrium analysis.