Perfectly Competitive Supply

Opportunity Cost and the Foundations of Individual Supply

• Foundation of Individual Supply Curves:

  • The supply curve for any good or service is rooted directly in an individual's microeconomic choice of whether to allocate time and resources toward producing that good versus pursuing alternative economic activities.

• Case Study: Recycling Container Collection (Harry's Search Decision):

  • Baseline Alternative Pursuit: Harry can earn $\$6.00\,\text{per hour}$ washing dishes. Therefore, Harry's opportunity cost of searching for soft drink containers is explicitly $\$6.00\,\text{per hour}$.
  • Diminishing Marginal Returns in Search: As search time increases, the additional (marginal) number of containers found per hour declines due to diminishing productivity.
  • Container Retrieval Schedule:
  • At $0\,\text{hours/day}$: Total containers = $0$, Additional containers = $0$.
  • At $1\,\text{hour/day}$: Total containers = $600$, Additional containers = $600$.
  • At $2\,\text{hours/day}$: Total containers = $1,000$, Additional containers = $400$.
  • At $3\,\text{hours/day}$: Total containers = $1,300$, Additional containers = $300$.
  • At $4\,\text{hours/day}$: Total containers = $1,500$, Additional containers = $200$.
  • At $5\,\text{hours/day}$: Total containers = $1,600$, Additional containers = $100$.

• Evaluating Hourly Marginal Benefit at a Deposit Price of $\$0.02$ ($2\,\text{cents}$) per Container:

  • Hourly benefit is calculated as additional containers found multiplied by the deposit price collected per container:

$\text{Hourly Benefit} = \Delta Q \times \text{Deposit Price}$

• First Hour: Finds $600$ additional containers. Earnings = $600 \times \$0.02 = \$12.00$. Since $\$12.00 > \$6.00$, searching yields $\$6.00$ more than washing dishes.

• Second Hour: Finds $400$ additional containers. Earnings = $400 \times \$0.02 = \$8.00$. Since $\$8.00 > \$6.00$, searching remains superior to dishwashing.

• Third Hour: Finds $300$ additional containers. Earnings = $300 \times \$0.02 = \$6.00$. At this exact point ($\$6.00 = \$6.00$), Harry is indifferent between searching for containers and washing dishes.

• Fourth Hour: Finds $200$ additional containers. Earnings = $200 \times \$0.02 = \$4.00$. Since $\$4.00 < \$6.00$, Harry will not search a fourth hour.

• Fifth Hour: Finds $100$ additional containers. Earnings = $100 \times \$0.02 = \$2.00$.

  • Determining Minimum Redemption Price to Induce Search Hours:

• The equation determining the minimum redemption price $p$ required to induce an additional hour of searching is:

$p \times \Delta Q = \$6.00$

• Minimum Price for a Second Hour: For the second hour, $\Delta Q = 400$.

p \times 400 = \6.00 \Rightarrow p = \frac{\6.00}{400} = \$0.015 \quad (1.5\,\text{cents/can})

• Individual Supply Curve Coordinates:
  • At $1\,\text{cent/can}$ ($\$0.01$): Supply = $600\,\text{cans/day}$ ($6$ in hundreds/day).
  • At $1.5\,\text{cents/can}$ ($\$0.015$): Supply = $1,000\,\text{cans/day}$ ($10$ in hundreds/day).
  • At $2\,\text{cents/can}$ ($\$0.02$): Supply = $1,300\,\text{cans/day}$ ($13$ in hundreds/day).
  • At $3\,\text{cents/can}$ ($\$0.03$): Supply = $1,500\,\text{cans/day}$ ($15$ in hundreds/day).
  • At $6\,\text{cents/can}$ ($\$0.06$): Supply = $1,600\,\text{cans/day}$ ($16$ in hundreds/day).

Deriving the Market Supply Curve

• Horizontal Summation:

  • Market supply curves are constructed by horizontally adding the quantity supplied by each individual seller at every given price point.

• Two-Seller Aggregation (Harry and Barry):

  • Assuming Harry and Barry have identical individual supply decisions:
  • At $1\,\text{cent/can}$, Harry supplies $600\,\text{cans/day}$ and Barry supplies $600\,\text{cans/day}$. Combined market supply = $600 + 600 = 1,200\,\text{cans/day}$.
  • At $1.5\,\text{cents/can}$, market quantity = $10 + 10 = 20$ ($2,000\,\text{cans/day}$).
  • At $2\,\text{cents/can}$, market quantity = $13 + 13 = 26$ ($2,600\,\text{cans/day}$).
  • At $3\,\text{cents/can}$, market quantity = $15 + 15 = 30$ ($3,000\,\text{cans/day}$).
  • At $6\,\text{cents/can}$, market quantity = $16 + 16 = 32$ ($3,200\,\text{cans/day}$).

• Scaling to $1,000$ Identical Sellers:

  • To aggregate across $1,000$ identical suppliers, multiply each quantity value on the individual supply curve by $1,000$:
  • At $1\,\text{cent/can}$: Market quantity = $600,000\,\text{cans/day}$ ($6$ in $100,000\text{s}$/day).
  • At $1.5\,\text{cents/can}$: Market quantity = $1,000,000\,\text{cans/day}$ ($10$ in $100,000\text{s}$/day).
  • At $2\,\text{cents/can}$: Market quantity = $1,300,000\,\text{cans/day}$ ($13$ in $100,000\text{s}$/day).
  • At $3\,\text{cents/can}$: Market quantity = $1,500,000\,\text{cans/day}$ ($15$ in $100,000\text{s}$/day).
  • At $6\,\text{cents/can}$: Market quantity = $1,600,000\,\text{cans/day}$ ($16$ in $100,000\text{s}$/day).

• Economic Foundations of Upward-Sloping Supply Curves:

  • Low-Hanging Fruit Principle: Individuals exploit their most attractive, lowest-cost opportunities first before expanding into higher-cost production.
  • Differences in Opportunity Costs: Different potential market participants face varying opportunity costs; higher prices attract individuals with higher opportunity costs into the market.

Characteristics of Imperfect vs. Perfectly Competitive Markets

• Core Definitions:

  • Profit: The difference between total revenue and total cost ($\text{Profit} = TR - TC$).
  • Profit-Maximizing Firm: A firm whose primary operational objective is to maximize total profit.
  • Perfectly Competitive Market: A market structure in which no individual buyer or seller has influence over the prevailing market price.
  • Price Taker: An individual or firm that must accept the equilibrium market price established by industry demand and supply.

• Four Characteristics of Perfectly Competitive Markets:

  1. Standardized Product: All firms produce and sell homogenous, identical products.
  2. Many Buyers and Sellers: Each market participant buys or sells only a minuscule fraction of total market volume.
  3. Mobile Productive Resources: Capital, labor, and other production inputs can freely move into or out of the industry.
  4. Well-Informed Participants: Buyers and sellers possess complete and accurate information regarding prices and products.

• Industry Approximations:

  • The market for wheat closely approximates perfect competition.
  • The market for desktop computer operating systems (e.g., Macintosh and Linux) does not approximate perfect competition.

• Firm Choice under Competition:

  • Competitive firms have zero control over market price; market price is determined by the intersection of industry supply and demand curves.
  • The primary challenge for the competitive firm is choosing its short-run output level $Q$ to maximize total profit at the market price P$.\n\n# Short-Run Production Concepts and Cost Structures\n\n* **Production Definitions:**\n * **Factor of Production:** An input used in the production process (e.g., labor, capital, machinery).\n * **Short Run:** A production period during which at least one factor of production is fixed.\n * **Long Run:** A period long enough that all factors of production can be varied.\n * **Fixed Factor of Production:** An input whose quantity cannot be altered in the short run.\n * **Variable Factor of Production:** An input whose quantity can be adjusted in the short run to change output levels.\n * **Law of Diminishing Returns:** When additional units of a variable input are added to fixed inputs, the marginal output generated per additional unit of variable input eventually declines.\n\n* **Cost Definitions:**\n * **Fixed Cost (FC):** Costs associated with fixed factors of production that do not vary with output volume.\n * **Variable Cost (VC):** Costs associated with variable factors of production that vary directly with output volume.\n * **Total Cost (TC):** The sum of fixed and variable costs:\n\nTC = FC + VC\n\n * **Marginal Cost (MC):** The change in total cost resulting from producing one additional unit of output:\n\nMC = \frac{\Delta TC}{\Delta Q}\n\n * **Average Variable Cost (AVC):** Variable cost divided by output quantity:\n\nAVC = \frac{VC}{Q}\n\n * **Average Total Cost (ATC):** Total cost divided by output quantity:\n\nATC = \frac{TC}{Q}\n\n# Comprehensive Production and Cost Data Analysis\n\n* **Employee and Output Schedule (Glass Bottle Maker):**\n\n\n\n * 0\,\text{employees/day} \Rightarrow 0\,\text{bottles/day}\n * 1\,\text{employee/day} \Rightarrow 80\,\text{bottles/day}\n * 2\,\text{employees/day} \Rightarrow 200\,\text{bottles/day}\n * 3\,\text{employees/day} \Rightarrow 260\,\text{bottles/day}\n * 4\,\text{employees/day} \Rightarrow 300\,\text{bottles/day}\n * 5\,\text{employees/day} \Rightarrow 330\,\text{bottles/day}\n * 6\,\text{employees/day} \Rightarrow 350\,\text{bottles/day}\n * 7\,\text{employees/day} \Rightarrow 362\,\text{bottles/day}\n\n* **Cost Breakdown Schedule:**\n\n\n\n * Daily Fixed Cost (FC$) =$\$40.00\,\text{per day}.\n * Variable Cost (VC$) increases by$\$12.00\,\text{per day} for each additional employee.\n * Detailed Numerical Table:\n * 0\,\text{employees}$|$0\,\text{bottles}$|$FC = \$40$|$VC = \$0$|$TC = \$40$|$MC = \$0.15\n * 1\,\text{employee}$|$80\,\text{bottles}$|$FC = \$40$|$VC = \$12$|$TC = \$52$|$MC = \$0.10\n * 2\,\text{employees}$|$200\,\text{bottles}$|$FC = \$40$|$VC = \$24$|$TC = \$64$|$MC = \$0.20\n * 3\,\text{employees}$|$260\,\text{bottles}$|$FC = \$40$|$VC = \$36$|$TC = \$76$|$MC = \$0.30\n * 4\,\text{employees}$|$300\,\text{bottles}$|$FC = \$40$|$VC = \$48$|$TC = \$88$|$MC = \$0.40\n * 5\,\text{employees}$|$330\,\text{bottles}$|$FC = \$40$|$VC = \$60$|$TC = \$100$|$MC = \$0.60\n * 6\,\text{employees}$|$350\,\text{bottles}$|$FC = \$40$|$VC = \$72$|$TC = \$112$|$MC = 100\n * 7\,\text{employees}$|$362\,\text{bottles}$|$FC = \$40$|$VC = \$84$|$TC = \$124$|$MC = -\n\n* **Revenue and Profit Schedule (at Price P = \$0.35\,\text{per bottle}):**\n\n\n\n * Profit Formula:\n\n\text{Profit} = \text{Total Revenue} - \text{Total Cost} = TR - VC - FC\n\n * Output and Profit Values:\n * 0\,\text{employees}$($0\,\text{bottles}$):$TR = \$0.00$,$TC = \$40.00$,$\text{Profit} = -\$40.00\n * 1\,\text{employee}$($80\,\text{bottles}$):$TR = \$28.00$,$TC = \$52.00$,$\text{Profit} = -\$24.00\n * 2\,\text{employees}$($200\,\text{bottles}$):$TR = \$70.00$,$TC = \$64.00$,$\text{Profit} = \$6.00\n * 3\,\text{employees}$($260\,\text{bottles}$):$TR = \$91.00$,$TC = \$76.00$,$\text{Profit} = \$15.00\n * 4\,\text{employees}$($300\,\text{bottles}$):$TR = \$105.00$,$TC = \$88.00$,$\text{Profit} = \$17.00 (Maximum Profit)\n * 5\,\text{employees}$($330\,\text{bottles}$):$TR = \$115.50$,$TC = \$100.00$,$\text{Profit} = \$15.50\n * 6\,\text{employees}$($350\,\text{bottles}$):$TR = \$122.50$,$TC = \$112.00$,$\text{Profit} = \$10.50\n * 7\,\text{employees}$($362\,\text{bottles}$):$TR = \$126.70$,$TC = \$124.00$,$\text{Profit} = \$2.70\n\n* **Average Variable Cost (AVC$) and Average Total Cost ($ATC) Schedule:**\n\n\n\n * Detailed Per-Unit Cost Values:\n * 0\,\text{employees}$($0\,\text{bottles}$):$VC = \$0$,$AVC = - $,$TC = \$40$,$ATC = - $,$MC = - \n * 1\,\text{employee}$($80\,\text{bottles}$):$VC = \$12$,$AVC = \$0.15$,$TC = \$52$,$ATC = \$0.65$,$MC = \$0.15\n * 2\,\text{employees}$($200\,\text{bottles}$):$VC = \$24$,$AVC = \$0.12$,$TC = \$64$,$ATC = \$0.32$,$MC = \$0.10\n * 3\,\text{employees}$($260\,\text{bottles}$):$VC = \$36$,$AVC = \$0.138$,$TC = \$76$,$ATC = \$0.292$,$MC = \$0.20\n * 4\,\text{employees}$($300\,\text{bottles}$):$VC = \$48$,$AVC = \$0.16$,$TC = \$88$,$ATC = \$0.293$,$MC = \$0.30\n * 5\,\text{employees}$($330\,\text{bottles}$):$VC = \$60$,$AVC = \$0.182$,$TC = \$100$,$ATC = \$0.303$,$MC = \$0.40\n * 6\,\text{employees}$($350\,\text{bottles}$):$VC = \$72$,$AVC = \$0.206$,$TC = \$112$,$ATC = \$0.32$,$MC = \$0.60\n * 7\,\text{employees}$($362\,\text{bottles}$):$VC = \$84$,$AVC = \$0.232$,$TC = \$124$,$ATC = \$0.343$,$MC = 100\n\n# Profit Maximization Rules and Short-Run Shutdown Conditions\n\n* **Maximum-Profit Condition:**\n * A perfectly competitive firm maximizes short-run profit by selecting output where price equals marginal cost:\n\n\text{Price} = \text{Marginal Cost} \quad (P = MC)\n\n* **Profit-Maximizing Decision Rules:**\n * **If P > MC:** Expanding output increases total profit because additional revenue exceeds additional cost.\n * **If P < MC:** Reducing output increases total profit because cost reductions exceed revenue loss.\n\n* **Short-Run Shutdown Conditions:**\n * **Primary Condition:** A firm shuts down in the short run if total revenue is strictly less than total variable cost at all output levels:\n\nP \times Q < VC \quad \text{for all levels of } Q\n\n * **Unit-Cost Condition:** Equivalently, the firm shuts down if market price drops below minimum average variable cost:\n\nP < \min(AVC)\n\n# Graphical Analysis of Profit and Loss\n\n* **Measuring Profit Graphically:**\n * Total profit is computed geometrically as:\n\n\text{Profit} = (P - ATC) \times Q\n\n * Graphically, profit equals the area of a rectangle with height (P - ATC)$and width$Q$.

• Positive Profit Case:

  • At price $P = \$0.20\,\text{per bottle}$, output $Q = 260\,\text{bottles/day}$, and $ATC = \$0.12\,\text{per bottle}$:
  • Profit per unit = $P - ATC = \$0.20 - \$0.12 = \$0.08\,\text{per bottle}$.
  • Total daily profit = \0.08 \times 260 = \$20.80\,\text{per day}$.
  • Average revenue ($AR$) equals marginal revenue ($MR$) equals price ($P$). Profit is represented by rectangle $ABCD$.

• Negative Profit / Loss Minimization Case:

  • When price is less than $ATC$ at the output level where $P = MC$, the firm experiences a short-run economic loss equal to (ATC - P) \times Q$.\n * **Short-Run Production Decision:** If P < ATC$but$P > \min(AVC), the firm continues producing in the short run because total revenue exceeds variable cost, offsetting a portion of fixed costs.\n * At price P = \$0.08\,\text{per bottle}$, output$Q = 180\,\text{bottles/day}$, and$ATC = \$0.10\,\text{per bottle}:\n * Profit per unit = P - ATC = \$0.08 - \$0.10 = -\$0.02\,\text{per bottle}.\n * Total daily profit = -\0.02 \times 180 = -\3.60\,\text{per day}$(a loss of$\$3.60\,\text{per day}).\n\n# The Individual Supply Curve and the Cost Side of the Market\n\n* **Derivation of Short-Run Supply Curve:**\n * For a perfectly competitive firm (or any seller operating where output can be sold at a constant market price), the individual short-run supply curve coincides exactly with the segment of its Marginal Cost (MC$) curve that lies above its Average Variable Cost ($AVC$$) curve.

• Market Side Duality:

  • The market supply curve represents the cost side of the market (marginal cost of production).
  • The market demand curve represents the benefit side of the market (marginal benefit to consumers).

Academic References

• Frank, H. R., & Bernanke, B. (2009). Principles of Microeconomics (4th ed.). New York, USA: McGraw-Hill/Irwin.