Chapter 6: Sellers and Incentives — Notes

6.1 Sellers in a Perfectly Competitive Market

  • Conditions of a perfectly competitive market:

    • No buyer or seller is big enough to influence market price (many buyers and sellers)

    • Sellers produce identical goods

    • Free entry and exit in the market

  • In such markets, individual firms are price takers and cannot set the price; they choose how much to produce to maximize profits.

6.2 The Seller’s Problem

  • Goal: Maximize Profit

  • A seller must solve three problems:

    • 1) How to make the product (production: turning inputs into outputs)

    • 2) What is the cost of making the product (cost of production)

    • 3) How much can the seller get for the product in the market (revenue)

  • Production concepts:

    • Production is the process of transforming inputs into outputs.

    • Physical capital: any good used for production (machines, buildings).

    • Short run vs. long run:

    • Short run: some inputs cannot be changed (e.g., you can’t buy another oven today).

    • Long run: all inputs can be changed (you can build or buy more capacity).

    • Variable factor of production: inputs that can be changed in the short run and change with output.

    • Fixed factor of production: inputs that cannot be changed in the short run.

    • Overhead is another term for fixed costs.

  • Marginal product (MP):

    • MP is the change in total output associated with using one more unit of input.

    • Growth in MP initially due to Specialization (workers becoming more efficient when they specialize and work together).

    • Law of diminishing returns: MP eventually falls as more units of input are added when some inputs are fixed.

    • MP can be negative if too many workers crowd a fixed-capital environment.

  • Short-run production data (Exhibit 6.1):

    • Output per day, number of workers, and MP illustrate MP trends and the possibility of negative MP when input starts to crowd fixed factors.

  • Costs of production (short run):

    • Total Cost (TC) = Variable Cost (VC) + Fixed Cost (FC)

    • Variable costs change with output; fixed costs do not.

    • Average costs:

    • Average Total Cost (ATC) = TC / Q

    • Average Variable Cost (AVC) = VC / Q

    • Average Fixed Cost (AFC) = FC / Q

  • The seller’s problem: 3 parts revisited in cost terms

    • 1) How to make the product (production function, MP, short-run vs long-run choices)

    • 2) What are the costs (VC, FC, TC; ATC, AVC, AFC; MC)

    • 3) How much can be sold for (revenue, price, MR in perfect competition)

  • Marginal cost (MC):

    • MC = ΔTC / ΔQ (change in total cost from producing one more unit)

  • Revenue and pricing in perfect competition:

    • Total Revenue (TR) = Price × Quantity sold: TR=PimesQTR = P imes Q

    • In perfect competition, MR = ΔTR / ΔQ = P

  • The seller’s problem in revenue terms:

    • Profit (economic profit) = TR − TC

    • Profit can be written as: extProfit=(P−ATC)imesQext{Profit} = (P - ATC) imes Q when price is used for revenue and ATC is the average total cost at the output level Q.

    • The firm decides the quantity where MR = MC (in perfect competition: P = MC).

    • After choosing Q, compare P to ATC to determine economic profit or loss.

  • The marginal approach to production decisions:

    • The firm expands production up to the point where MR = MC.

    • In perfect competition, MR = P, so the profit-maximizing condition is P=MCP = MC at the optimal quantity.

6.3 From the Seller’s Problem to the Supply Curve

  • The supply decision is reflected in the marginal decision rule: MC = Price (MR = MC) for profit maximization.

  • Is MC always the firm’s supply curve? Not necessarily for all prices; a firm supplies only if it covers its variable costs.

  • Price responsiveness (elasticity of supply):

    • Elasticity of supply (Es) measures how responsive quantity supplied is to price changes:

    • Es=%ΔQs%ΔPEs = \frac{\% \Delta Q_s}{\% \Delta P}

  • Arc elasticity (short-cut method) for calculating Es: use changes over a price interval to approximate elasticity.

  • Types of supply elasticity:

    • Elastic supply: Es > 1

    • Inelastic supply: Es < 1

    • Unit-elastic supply: Es=1Es = 1

  • Different supply curves (illustrative): perfectly elastic, unit-elastic, and perfectly inelastic curves.

  • Factors affecting elasticity of supply include:

    • Inventory levels, ease of hiring, and the time horizon.

  • Shutdown vs. production decisions:

    • Short-run decision to harvest or produce hinges on whether price covers variable costs.

    • Shutdown rule: shut down if price < AVC; operate if price > AVC.

  • Short-run supply curve: the portion of MC above the shutdown point (above AVC).

  • Sunk costs concept:

    • Fixed costs are sunk in the short run and should not affect current production decisions.

6.4 Producer Surplus

  • Producer surplus is the difference between the price a firm would be willing to accept and the market price, or equivalently the area below price and above the supply (MC) curve.

    • Exhibit illustrates how to measure producer surplus and how it relates to the market price.

  • Producer surplus can be visualized as the area under the price line and above the marginal cost curve up to the quantity sold.

6.5 From the Short Run to the Long Run

  • Key distinction:

    • Short run: some inputs (and thus some costs) are fixed.

    • Long run: all inputs and costs are variable; firms can adjust all factors of production.

  • What changes in the long run:

    • Firms can adjust capital: build new plants, retire old ones, alter plant size.

  • Economies of scale, constant returns to scale, and diseconomies of scale:

    • Economies of scale: ATC falls as output increases; reasons include specialization and large setup benefits.

    • Constant returns to scale: ATC unchanged as output increases.

    • Diseconomies of scale: ATC rises as output increases; may arise from management problems, coordination costs, etc.

  • Short-run vs. long-run supply curves:

    • Short-run supply can differ from long-run supply because in the long run firms can enter or exit; entering firms earn profits attract more supply, while losses drive exits.

6.6 From the Firm to the Market: Long-Run Competitive Equilibrium

  • Long-run entry and exit move profits toward zero economic profit when there is free entry/exit and no barriers.

  • The long-run equilibrium condition in a competitive market with free entry/exit:

    • Price (P) equals the minimum of Average Total Cost (ATC) so that economic profits are zero.

  • Example scenario (corn vs. soybeans):

    • A profit comparison in the long run can yield different conclusions for accountants vs. economists when considering opportunity costs; economists count implicit costs to determine economic profit.

  • Market adjustments after demand shifts:

    • In the long run, entry or exit adjusts the supply, moving price toward the zero-profit level.

  • Further illustrations show how long-run supply can become horizontal under certain assumptions about perfect competition and free entry/exit.

Evidence-Based Economics

  • Question: How would an ethanol subsidy affect ethanol producers?

    • Subsidies change short-run profits and can affect entry/exit, market price, and industry composition.

    • Exhibit shows relationships between subsidy, plant numbers, and market dynamics.

  • Problems and thought experiments (Exhibit 6.22 and related material):

    • The price–quantity table for ethanol with and without subsidies illustrates how subsidies raise profits and attract entry, then potentially reduce profits as more entrants join and price adjusts.

  • Key takeaway: subsidies influence short-run profits and incentives, but long-run outcomes depend on market adjustments (entry/exit) and price changes.

From the Wisconsin Cheeseman: Production and Cost Exhibits (Illustrative Examples)

  • Exhibit 6.1: Production data illustrating the production function, marginal product, and how output changes with labor.

  • Exhibit 6.2: Short-run production function visualization showing MP and the effect of fixed capital on output.

  • Exhibit 6.3: Costs of production table including:

    • Output per day (Q)

    • Number of employees (L)

    • Marginal product (MP)

    • Variable cost (VC)

    • Fixed cost (FC)

    • Total cost (TC) = VC + FC

    • Average total cost (ATC) = TC / Q

    • Average fixed cost (AFC) = FC / Q

    • Average variable cost (AVC) = VC / Q

    • Marginal cost (MC) = ΔTC / ΔQ

  • These exhibits illustrate how MC, ATC, and AVC interact, how costs change with output, and how profits are determined by the relationship between price and costs.

Key Formulas and Concepts (summary with LaTeX)

  • Total Revenue: TR=P×QTR = P \times Q

  • Total Cost: TC=VC+FCTC = VC + FC

  • Average Total Cost: ATC=TCQATC = \frac{TC}{Q}

  • Average Variable Cost: AVC=VCQAVC = \frac{VC}{Q}

  • Average Fixed Cost: AFC=FCQAFC = \frac{FC}{Q}

  • Marginal Cost: MC=ΔTCΔQMC = \frac{\Delta TC}{\Delta Q}

  • Profit (economic): π=TR−TC=(P×Q)−TC\pi = TR - TC = (P \times Q) - TC

  • Profit in terms of ATC: π=(P−ATC)×Q\pi = (P - ATC) \times Q

  • Profit-maximizing condition in perfect competition: MR=MCand since MR=P:P=MCMR = MC \quad\text{and since } MR = P: \quad P = MC

  • Shutdown rule (short run): shut down if P < AVC; operate if P > AVC

  • Producer surplus: area below price and above the MC curve (supply curve in competitive markets)

  • Elasticity of supply: Es=%ΔQs%ΔPEs = \frac{\% \Delta Q_s}{\% \Delta P}

  • Long-run competitive equilibrium idea: with free entry/exit, economic profits tend toward zero; price tends to equal the minimum of ATC in the long run.

Connections and Implications

  • The three-part seller problem connects directly to the supply decision: supply reflects how firms respond to prices given production technology and costs.

  • Marginal decision making (MR = MC) is the core mechanism behind supply curves and profit maximization in competitive markets.

  • Producer surplus and profits link firm-level decisions to market outcomes; entry/exit drives long-run adjustment toward zero economic profits.

  • The distinction between accounting profit and economic profit matters for understanding incentives to enter/exit markets and to allocate resources efficiently.

  • The elasticity of supply affects how quickly and by how much quantity supplied responds to price changes, influencing short-run and long-run market dynamics.

Quick reference: Key relationships to remember

  • Production and costs:

    • TC = VC + FC

    • ATC = TC / Q, AVC = VC / Q, AFC = FC / Q

    • MC = ΔTC / ΔQ

  • Revenue and profit:

    • TR = P × Q

    • π = TR − TC

    • π = (P − ATC) × Q

  • Profit maximization in perfect competition:

    • MR = MC, with MR = P

  • Costs vs. shutdown:

    • Stay open if P ≥ AVC; shut down if P < AVC

  • Long-run equilibrium with free entry/exit:

    • P tends toward minimum ATC; economic profits approach zero

  • Producer surplus and areas under curves:

    • Producer surplus = area above MC and below price

  • Elasticity of supply:

    • Es = (%ΔQ_s) / (%ΔP)

  • Economies vs. diseconomies of scale:

    • Economies of scale reduce ATC with larger output; diseconomies increase ATC with larger output

Title

Chapter 6: Sellers and Incentives — Comprehensive Notes (S&R-6)