Chapter 6 Notes: Sellers and Incentives

6.1 Sellers in a Perfectly Competitive Market

  • Three defining conditions of a perfectly competitive market:

    • No buyer or seller is large enough to influence the market price.

    • Sellers produce identical goods.

    • There is free entry and exit in the market.

  • Price-taking behavior:

    • In perfect competition, individual firms are price-takers because each firm sells only a tiny fraction of total market output.

    • The market price is determined by the collective actions of all buyers and sellers; an individual firm cannot set or influence it.

  • Intuition and examples:

    • A farmer deciding to grow corn vs. soybeans does not affect world prices; if all farmers switch to corn, prices would fall for corn and rise for soybeans.

    • Markets like eBay illustrate entry/exit flexibility; many markets permit free entry and exit in practice.

  • Implications for policy and business:

    • Understanding seller decisions under perfect competition helps predict responses to policies (e.g., subsidies, taxes) and to entrepreneurial opportunities.

6.2 The Seller's Problem

  • The seller's objective:

    • Maximize net benefits, i.e., profits.

    • Three components of the seller's problem: making the goods, the cost of doing business, and the rewards of doing business.

  • Production function:

    • Relationship between inputs used and outputs produced; transformation from inputs (e.g., labor, capital) to outputs (goods/services).

    • Firm concept: a firm produces and sells; can be a large organization or a single person.

  • The Wisconsin Cheeseman as a real-life example:

    • Inputs: labor (to pack cheese boxes) and physical capital (equipment/buildings).

    • Short run vs long run:

    • Short run: some inputs fixed (physical capital); labor is variable.

    • Long run: all inputs are variable; firm can adjust size and capital.

  • Key terminology:

    • Physical capital: machines and buildings used for production.

    • Short run: a period in which some inputs cannot be varied (fixed inputs).

    • Long run: a period in which all inputs can be varied.

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

    • Variable factor of production: input that can be changed in the short run.

  • The short-run production function and marginal product:

    • Exhibit 6.1 (The Cheeseman): output varies with number of workers; marginal product (MP) is the additional output from one more unit of input:MP=racextΔQextΔLMP= rac{ ext{Δ}Q}{ ext{Δ}L}

    • MP behavior:

    • MP can initially rise with the first few workers due to specialization and division of labor.

    • Specialization example: Subway assembly line; workers specialize in specific steps to boost productivity.

    • MP eventually decreases as more workers are added (Law of Diminishing Returns): with a fixed amount of capital, adding workers leads to smaller increments in output.

    • The last worker can even reduce total output if too many workers create congestion or get in each other’s way.

  • The cost of doing business: introducing cost curves

    • Total cost (TC) = Variable cost (VC) + Fixed cost (FC):TC=VC+FCTC=VC+FC

    • Variable costs: vary with output (e.g., wages for workers).

    • Fixed costs: do not vary with output in the short run (e.g., buildings, machinery).

    • The Wisconsin Cheeseman numbers (illustrative):

    • Workers’ daily wage = $72; 8 hours per day; VC increases by $72 per additional worker.

    • Fixed cost (cost of structures/machinery) = $200 per day.

    • Thus, VC and FC are specified for different output levels; TC is VC+FC.

    • Cost per unit measures:

    • Average total cost (ATC) = ATC=racTCQATC = rac{TC}{Q}

    • Average variable cost (AVC) = AVC=racVCQAVC = rac{VC}{Q}

    • Average fixed cost (AFC) = AFC=racFCQAFC = rac{FC}{Q}

    • Example values (The Cheeseman at Q = 321):

    • Total cost (TC) = $416 → ATC = rac416321=1.29rac{416}{321}=1.29

    • Average variable cost (AVC) = $0.67

    • Average fixed cost (AFC) = $0.62

    • Hence, ATC=AVC+AFC=0.67+0.62=1.29ATC = AVC + AFC = 0.67 + 0.62 = 1.29

    • Marginal cost (MC): the change in total cost from producing one more unit:

    • MC=racextΔTCextΔQMC = rac{ ext{Δ}TC}{ ext{Δ}Q}

    • At Q = 321, MC = $0.63 for the 321st unit.

    • Relationship between MC and cost curves:

    • MC is below ATC and AVC when ATC and AVC are falling; MC is above them when ATC and AVC are rising. This explains why MC intersects ATC and AVC at their minimums.

    • Intuition example: adding a new item to a basket with average price rises the basket’s average price if the new item is priced above the current average; analogous intuition for MC crossing ATC/AVC.

  • The rewards of doing business: revenue concepts

    • Revenue (TR) = price × quantity:TR=PimesQTR = P imes Q

    • In perfectly competitive markets, sellers are price-takers, so price equals marginal revenue (MR):MR=racextΔTRextΔQ=PMR = rac{ ext{Δ}TR}{ ext{Δ}Q} = P

    • The “good stuff” for profits comes from comparing TR to TC.

  • Profit definitions

    • Profit (economic profit) = TR − TC

    • Accounting profits = TR − explicit costs (e.g., wages, materials, depreciation)

    • Economic profits = TR − (explicit costs + implicit costs, e.g., opportunity costs of owner’s time)

  • From the seller's problem to the supply curve

    • The MR = MC rule links market price to the MC curve to determine short-run output:

    • A firm’s supply curve shows the quantity supplied as a function of price.

  • Price elasticity of supply

    • Measure of how responsive quantity supplied is to price changes:extpriceelasticityofsupply ε<em>s=racextPercentagechangeinQ</em>sextPercentagechangeinpriceext{price elasticity of supply} \ ε<em>s= rac{ ext{Percentage change in }Q</em>s}{ ext{Percentage change in price}}

    • Typically positive: higher price → more quantity supplied.

    • Elasticities range from perfectly elastic (∞) to perfectly inelastic (0) to unit-elastic (1).

    • Perfectly elastic supply: a tiny price change leads to an infinite change in quantity supplied.

    • Unit-elastic supply: a 1% increase in price leads to a 1% increase in quantity supplied.

    • Determinants of supply elasticity:

    • Availability of inventories (extensibility to ramp up production)

    • Time to respond (longer time → more elastic)

    • Availability of labor (easier hiring) → more elastic

  • Shutdown and sunk costs

    • Shutdown: a short-run decision to stop producing for a period.

    • In Exhibit 6.10, a price of $0.59 may lead MR = MC to a positive output but the firm might still shut down if price cannot cover variable costs.

    • Sunk costs: costs that cannot be recovered once incurred (e.g., a fixed lease). Decisions in the short run should ignore sunk costs when choosing current production levels; only variable costs matter for the shutdown decision.

  • Producer surplus (PS)

    • PS measures the seller’s gain from participating in the market, analogous to consumer surplus.

    • Defined as the area above the MC curve and below the market price: PS = (Price − MC) integrated over the quantity sold.

    • PS is distinct from economic profits because PS does not account for total costs beyond MC; it only uses the MC as the relevant supply curve boundary.

6.5 From the Short Run to the Long Run

  • Long run is the period in which all inputs are variable, and firms can adjust the size of their plant and the mix of inputs.

    • In the long run, firms choose the optimal combination of labor and capital to minimize ATC for each output level.

    • Long-run cost curves are derived from the envelope of short-run cost curves and reflect the scale of operation.

  • Economies, constants, and diseconomies of scale

    • Economies of scale: ATC falls as output rises within a certain range, due to increases in efficiency as plant size grows.

    • Constant returns to scale: ATC remains unchanged as output changes.

    • Diseconomies of scale: ATC rises as output increases beyond a certain level, possibly due to management inefficiencies or coordination problems.

  • Long-run vs short-run cost curves

    • The long-run average total cost (LRATC) curve is typically smoother and exhibits economies, constants, and diseconomies of scale as scale changes.

  • Long-run supply and exit rules

    • If the market price is below the minimum of the LRATC, firms have no incentive to stay in the industry and will exit in the long run.

    • Exit rule (long run): Exit if price is less than ATC or equivalently if total revenue is less than total cost.

  • The Cheeseman and long-run implications

    • In the long run, firms adjust to minimize ATC and to the level where profit is zero (economic profit = 0) in a competitive market.

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

  • Free entry and exit in the long run

    • With identical firms and constant input costs, free entry and exit push profits toward zero in long-run equilibrium.

    • Entry increases market supply, lowering price; exit decreases market supply, raising price.

  • Process of entry

    • Suppose price is above a firm’s minimum LRATC; new firms enter seeking profits.

    • Entry shifts market supply to the right, lowering price until it reaches the minimum LRATC; at that price, economic profits are zero, and no further entry occurs.

    • If the price remains above the minimum LRATC, additional firms enter until the price falls to the minimum LRATC.

  • Process of exit

    • If demand falls or costs rise, price can fall below LRATC; firms exit, shifting supply left and increasing price until it returns to the minimum LRATC.

  • Long-run equilibrium in a perfectly competitive industry

    • The long-run industry supply curve is horizontal at the level of the long-run minimum ATC.

    • Economic profits are zero in long-run equilibrium because entry/exit adjust supply to drive price to the LRATC minimum.

    • Accounting profits and economic profits diverge: zero economic profits do not imply zero accounting profits; owners are earning their opportunity costs in the economy.

  • Important caveats

    • The zero-profit result assumes identical firms with constant input costs. Heterogeneous firms or different cost structures can yield positive economic profits for some firms in long-run equilibrium; this is discussed further in the appendix.

  • Subsidies (brief note)

    • Subsidy: a payment or tax break used as an incentive for an agent to engage in an activity. Subsidies can affect firm behavior and may alter the long-run equilibrium by changing effective costs or the market price.

Summary of Core Points

  • Sellers optimize by solving the seller's problem on the margin: produce up to the point where MC = MR.

  • Short-run and long-run supply curves reflect a seller's willingness to sell at various prices; MC is central to determining supply.

  • Producer surplus is the area between the market price and the MC curve; it captures sellers' gains from trade beyond variable costs.

  • Free entry and exit in a perfectly competitive market drive long-run profits to zero, with price equaling the minimum of the long-run average total cost.

  • Economic profits account for both explicit and implicit costs, whereas accounting profits consider only explicit costs.

  • Understanding these rules helps explain both everyday business decisions and the likely effects of public policies, including subsidies and taxes.

Key Terms

  • firm: a business entity that produces and sells goods or services

  • production: the transformation of inputs into outputs

  • physical capital: machines and buildings used in production

  • short run: a period during which some inputs are fixed

  • long run: a period during which all inputs can be varied

  • fixed factor of production: an input that cannot be changed in the short run

  • variable factor of production: an input that can be changed in the short run

  • marginal product (MP): the change in output from adding one more unit of input

  • specialization: concentrating input use on a specific task to increase productivity

  • Law of Diminishing Returns: beyond a point, successive increases in inputs yield smaller increases in output

  • cost of production: total cost of inputs to produce a given output level

  • total cost (TC): VC + FC

  • variable cost (VC): costs that vary with output

  • fixed cost (FC): costs that do not vary with output in the short run

  • average total cost (ATC): ATC=racTCQATC = rac{TC}{Q}

  • average variable cost (AVC): AVC=racVCQAVC = rac{VC}{Q}

  • average fixed cost (AFC): AFC=racFCQAFC = rac{FC}{Q}

  • marginal cost (MC): MC=racextΔTCextΔQMC = rac{ ext{Δ}TC}{ ext{Δ}Q}

  • revenue (TR): TR=PimesQTR = P imes Q

  • marginal revenue (MR): MR=racextΔTRextΔQ=PextinaperfectlycompetitivemarketMR = rac{ ext{Δ}TR}{ ext{Δ}Q} = P ext{ in a perfectly competitive market}

  • profits: economic profits = TR − (explicit costs + implicit costs); accounting profits = TR − explicit costs

  • price elasticity of supply: ε<em>s=racextPercentagechangeinQ</em>sextPercentagechangeinpriceε<em>s= rac{ ext{Percentage change in }Q</em>s}{ ext{Percentage change in price}}

  • shutdown: a short-run decision to not produce for a period

  • sunk costs: costs that cannot be recovered once incurred; should not affect current decisions

  • producer surplus: area above the MC curve and below the market price

  • economies of scale: ATC falls as output increases

  • constant returns to scale: ATC unchanged with output

  • diseconomies of scale: ATC rises as output increases

  • free entry: no barriers to entering an industry

  • free exit: no barriers to exiting an industry

  • subsidy: a payment or tax break to incentivize an activity