Production, Costs, and Short-run vs Long-run: Lecture Notes

Overview of today's content: production and costs in microeconomic theory, focusing on how firms turn inputs into outputs, how costs arise, and how these cost structures shape profit-maximizing decisions in different market structures. The lecture contrasts short-run and long-run analysis and builds the toolkit (production functions, marginal/product concepts, and various cost curves) needed for more applied topics next week (revenue, demand, and profit maximization under different market structures). Key example used throughout: a Subway-style subs shop to illustrate production, specialization, and scaling effects.

Key concepts introduced

• Firm and production basics

  • A firm is an economic unit that takes factors of production and turns them into outputs to sell.
  • In models, the firm’s typical goal is profit maximization, defined as total revenue minus total costs.
  • Not all profits are the same: economic profit accounts for opportunity costs; accounting profit does not necessarily include these opportunity costs.
  • Economic profit = Total Revenue − Total Economic Cost; where Total Economic Cost = Explicit Costs + Implicit Costs (opportunity costs).
  • Other profit concepts include net profit, supernormal profit (often used synonymously with economic profit in some contexts), and normal profit (the minimum return sufficient to keep resources employed in the current use, i.e., the opportunity cost baseline for entrepreneurship).
  • Opportunity costs include foregone interest (the return from not investing capital elsewhere), economic depreciation (true decline in asset value), and the value of the owner’s time and alternative employment opportunities.
  • Normal profit is the minimum level of profit that would make a firm choose to operate rather than shut down, given risks and alternative opportunities.
  • Profit maximization in models typically assumes firms operate under constraints (technology and demand). In this week’s content, emphasis is on technology and production/cost structure; demand and revenue come into play in the next weeks.

• Technology and production concepts

  • Technology = the processes and methods a firm uses to convert inputs into outputs. This includes machinery, management practices, organizational methods, and even innovations like assembly lines.
  • A firm’s objective is to maximize economic profits, subject to constraints from technology and consumer demand.
  • Short run vs long run: a short run is a period in which some inputs are fixed (e.g., plant size, some capital like machines); the long run is a period sufficient to vary all inputs, adopt new technology, or resize the plant.
  • The long run concept is future-oriented: firms can choose among different production scales and technologies; the short run is one scenario within the long run planning horizon.
  • Example intuition: Subway store
  • In the short run, you can vary labor and some inputs (e.g., number of casual staff, ingredients) but the store size and fixed equipment (toasting machines, fridges) are fixed.
  • In the long run, you could move to a larger or smaller premises, changing fixed inputs entirely.

• Production function and the shapes you expect

  • Production function describes the physical relationship between inputs and outputs: Q = f(L, K, …), where L is labor (the variable input in the simple example) and K represents fixed inputs in the short run.
  • Short-run production function: some inputs fixed (e.g., store size, some machines). Vary labor to see how output changes.
  • Expected shape: with more workers, output generally increases, but not linearly due to specialization gains and fixed-capital bottlenecks.
  • Marginal product (MP) of labor: the additional output from an extra unit of input. If one worker yields 5 subs/hour and a second worker yields more than 5 additional subs (e.g., 7 more subs per hour), MP can rise due to specialization.
  • Average product (AP): output per unit of input, AP = Q / L. MP and AP are related but distinct; MP is the slope of the production function, while AP is the average level of output per worker.
  • Diminishing marginal returns (the law of diminishing returns): after some point, adding more input (labor) in the short run yields progressively smaller increases in output because fixed inputs (store size, machines) create bottlenecks and crowding.
  • Shape intuition for MP and AP
  • MP initially rises due to specialization and better task division, producing an inverted-U MP curve when viewed against quantity of input (or a rising MP when viewed along initial segments).
  • MP eventually declines due to congestion, bottlenecks, and diminishing returns to the fixed inputs.
  • AP rises with MP when MP > AP and falls when MP < AP; MP crosses AP at AP’s maximum.
  • Connection between production function and costs: the slope of the production function (MP) affects costs; higher MP means lower marginal cost (at least in simple one-input-cost models like wage = w, MC ≈ w / MP).

• Costs: fixed, variable, and total; and the associated average and marginal costs

  • Fixed costs (FC): do not vary with output in the short run (e.g., rent under a lease, some fixed capital). They can change in the long run with new leases or investments.
  • Variable costs (VC): vary with output (e.g., ingredients, hourly wages for casual labor, electricity used in production activities like toasting).
  • Total cost (TC): TC = FC + VC.
  • Average costs (per unit of output)
  • Average Fixed Cost (AFC): AFC = FC / Q
  • Average Variable Cost (AVC): AVC = VC / Q
  • Average Total Cost (ATC): ATC = TC / Q = AFC + AVC
  • Marginal cost (MC): the cost of producing one more unit of output. In discrete terms, MC = ΔTC / ΔQ; in calculus terms, MC = d(TC)/dQ. Since FC does not vary with output, ΔFC = 0 and MC ≈ ΔVC / ΔQ.
  • One-input-dominant example intuition (labor cost model): if wage is w and MP is the marginal product of labor, the marginal cost of producing an additional unit is roughly MC ≈ w / MP in the simple, single-variable-input framework.

• Short run cost shapes and their relationships

  • AFC is always downward-sloping due to fixed costs being spread over more units as Q increases; it is asymptotic to zero as Q → ∞.
  • AVC, ATC, and MC are typically U-shaped in the short run: they fall due to spreading fixed costs and initially rising due to increasing efficiency, then rise again as diminishing returns set in.
  • Key qualitative relationships on a cost diagram
  • MC intersects ATC at ATC’s minimum.
  • MC intersects AVC at AVC’s minimum.
  • ATC = AVC + AFC at all quantities.
  • The long-run perspective on costs reflects scale and technology choices rather than a single short-run curve. The long-run average cost (LRAC) is the envelope of all possible short-run average cost curves (i.e., the lower envelope of SRAC curves across different plant sizes/technologies).

• Long-run costs, economies of scale, and minimum efficient scale (MES)

  • Long-run average cost curve (LRAC) summarizes the lowest achievable average cost for each output level when a firm can adjust all inputs, including plant size and technology.
  • Economies of scale: LRAC falls as Q increases (cost advantages from large-scale production, specialization, bargaining power, fixed costs spread over more units, etc.).
  • Constant returns to scale: LRAC is flat over some range of Q; increasing output does not change average cost.
  • Diseconomies of scale: LRAC eventually rises as Q increases (coordination problems, communication costs, complexity, etc.).
  • MES (Minimum Efficient Scale): the smallest output level at which LRAC is minimized. MES helps explain market structure outcomes (e.g., monopoly vs. oligopoly vs. many small firms) because it indicates the scale at which costs are most efficiently produced.
  • If the LRAC curve is downward-sloping over a wide range, large-scale production is very efficient; if it has a flat or upward-sloping portion, there may be limits to the benefits of expanding output.
  • Illustration concept: a bookstore example with four sizes (small, medium, large, extra-large) to show how SRAC curves can differ by plant size; the LRAC curve would be the lower envelope of those SRAC curves, forming a smooth curve if sizes are continuous.

• Practical connections and implications for market structure

  • The shapes of SRAC and LRAC curves, plus MES, influence industry structure (e.g., whether a single firm dominates, or many small firms compete, or a few large firms dominate).
  • The link between cost curves and profit-maximizing decisions under different market structures (perfect competition, monopoly) is the focus of next week’s topics; the current week builds the cost-side toolset for those analyses.

• Numerical and algebraic relationships (summary of formulas)

  • Revenue and profit
  • Total Revenue: TR = P imes Q
  • Profit (economic): ext{Profit} = TR - TC
  • Economic cost: TC = FC + VC; TC = ext{Explicit Costs} + ext{Implicit Costs}
  • Economic profit: ext{EP} = TR - TC{ ext{economic}} where TC{ ext{economic}} = ext{Explicit} + ext{Implicit costs}
  • Normal profit: the minimum profit necessary to keep resources in their current use (the opportunity cost of entrepreneurship).
  • Cost curves
  • AFC: AFC = rac{FC}{Q}
  • AVC: AVC = rac{VC}{Q}
  • ATC: ATC = rac{TC}{Q} = rac{FC}{Q} + rac{VC}{Q} = AFC + AVC
  • MC: MC = rac{ΔTC}{ΔQ} ext{ (discrete) or } MC = rac{dTC}{dQ} ext{ (continuous)}
  • Relationship with variable costs: since ΔFC = 0, we also have MC = rac{ΔVC}{ΔQ}.
  • Production function and marginal concepts
  • Production function: Q = f(L, K, ext{…})
  • MP of labor: MP_L = rac{∂Q}{∂L}
  • AP of labor: AP_L = rac{Q}{L}
  • MP vs AP relationship: MP rises with early specialization, then eventually declines due to diminishing returns; MP crosses AP at AP’s maximum.
  • Long-run envelope concept
  • LRAC(Q) equals the lower envelope of all SRAC curves across different plant sizes/technologies.
  • If plant sizes vary continuously, LRAC is a smooth curve rather than a lumped set of lines.
  • Special cases and caveats
  • While the typical shapes are described (AFC downward; AVC/ATC/U-shaped; MC also U-shaped), there can be exceptions depending on production technology and industry specifics.

Key takeaways to remember for exams

• The production function links inputs to outputs; MP initially increases due to specialization, then declines due to diminishing returns.
• Cost curves (FC, VC, TC; AFC, AVC, ATC; MC) have predictable relationships: AFC falls with output; ATC and AVC are typically U-shaped; MC intersects ATC at ATC’s minimum and intersects AVC at AVC’s minimum.
• Long-run costs reflect the planner’s choice among plant sizes and technologies; LRAC is the envelope of SRAC curves and displays economies, constant returns, or diseconomies of scale; MES identifies the efficient scale of production.
• Economic profit accounts for opportunity costs; profits can be zero in the sense of economic profit, even when accounting profit is positive, if owners’ alternative opportunities are sufficiently valuable.
• These cost structures set the stage for analyzing firm behavior in different market structures in subsequent topics (perfect competition, monopoly, and the in-between cases).

Example takeaway visuals to practice

• Production function shape: MP vs Q is inverted-U; AP vs Q (forward-looking) peaks where MP crosses AP.
• Cost curves: AFC declines with Q; MC typically declines then rises; ATC follows a similar U-shape, crossing MC at its minimum; AVC also crosses MC at its own minimum.
• Long-run envelope: imagine several short-run cost curves for different plant sizes; the LRAC at each Q is the minimum of those SRAC values, forming a lower envelope.

Notes on the lecture framing and practical implications

• The lecture emphasizes building the toolkit (production functions and various cost curves) before integrating revenue and demand in later sessions to address profit-maximizing behavior.
• The Subway store narrative is used to illustrate how division of labor, specialization, and bottlenecks shape marginal product and thus marginal cost, reinforcing the intuition behind the mathematical relationships.
• The material deliberately distinguishes short-run phenomena (where some inputs are fixed) from long-run planning (where all inputs can be adjusted), highlighting that decision-making in real firms is often about choosing among different short-run configurations with an eye toward long-run costs and efficiency.

Ethical and real-world relevance considerations

• Opportunity costs remind decision-makers that resources have alternative uses; choosing one venture over another involves forgone wages, interest, or alternative business opportunities.
• Economies of scale and MES have implications for competition and market structure; very large firms may enjoy cost advantages that influence barriers to entry, pricing, and welfare. Policy implications (not deeply covered here) include considerations of monopolistic tendencies and the efficiency of resource allocation in industries with high MES.
• The distinction between economic and accounting profits highlights that a business can appear profitable on the books while still not providing an opportunity-cost-justified return, which has implications for investment and entrepreneurship decisions.

Summary of the core relationship map (conceptual)

• Q = f(L, FixedInputs) → MP governs the rate of output change per extra unit of input.
• Costs are FC + VC; outputs spread FC across Q reduces AFC; VC expands with Q depending on MP.
• MC = ΔTC/ΔQ, and in simple labor-only cases, MC ≈ w/MP.
• ATC = AFC + AVC; MC intersects ATC at the minimum of ATC; intersects AVC at the minimum of AVC.
• The LRAC curve is the envelope of SRAC curves and reveals the long-run efficiency and scale effects (economies, constant returns, diseconomies).

Key formulas for quick reference (LaTeX)

• TR = P imes Q
• TC = FC + VC
• ext{Profit}{economic} = TR - TC{ ext{economic}}
• ext{Explicit Costs} + ext{Implicit Costs} = TC_{ ext{economic}}
• AFC = rac{FC}{Q}
• AVC = rac{VC}{Q}
• ATC = rac{TC}{Q} = AFC + AVC
• MC = rac{ΔTC}{ΔQ} = rac{ΔVC}{ΔQ}
• For a single-variable input (labor) with wage w and marginal product MPL: MC ext{ (approx)} = rac{w}{MPL}
• Long-run cost envelope concept: LRAC(Q) = ext{min}ig ext{SRAC}_i(Q)igig) across all plant sizes i.
• MES: the minimum efficient scale, i.e., the smallest Q where LRAC is minimized.

End of notes