Notes on Production Costs, Short Run vs Long Run, and Economic vs Accounting Costs

Production Costs, Capacity, and Profit‑Maximizing Decisions

  • The lecture emphasizes efficiency limits due to inputs and capacity.
  • Example: two workers cannot produce 34 pairs of jeans; beyond a certain point, adding more inputs yields no additional output and wastes money.
  • H contributes the same as g; avoid hiring more inputs than needed because some inputs may be fixed and provide no additional value.
  • Intuition: diminishing marginal physical product (DMPP) means output eventually has a ceiling (capacity). Producing beyond capacity doesn’t add value.
  • Capacity is described as the ceiling on output (a valve/limit analogy): you can’t produce beyond what the inputs and space allow.
  • The “friends of the family syndrome”: fixed inputs that cannot be changed in the short run lead to inefficiencies if you over-hire or over-commit resources.
  • Short run vs. long run:
    • Short run: at least some inputs are fixed; fixed costs exist and some inputs cannot be changed.
    • Long run: all inputs can be varied; firms can adjust plant/equipment and scale decisions.
  • Startup business caveat: there’s no fixed period where inputs are completely fixed—startups may need to scale differently, but the framework still uses short run vs long run concepts.
  • Goal in production: maximize profit, not simply maximize output. Find the output level where profit is greatest, which depends on costs and revenues.

Costs: Total, Fixed, Variable, and Cost Curves

  • Total Cost (TC): the market value of all resources used to produce a good.
    • For example, TC = 245 (dollars) to produce 15 pairs of jeans.
    • This includes both fixed and variable costs.
  • Fixed Cost (FC): costs that do not change with output in the short run; must be paid even if production is zero.
    • Example: FC = 100 (cost of the factory).
  • Variable Cost (VC): costs that change with the rate of output; VC increases as output increases; at zero output, VC = 0.
  • Relationship: TC = FC + VC.
  • Average Total Cost (ATC): cost per unit of output.
    • ATC = rac{TC}{Q}
    • If TC = 245 and Q = 15, then ATC = rac{245}{15} \approx 16.33 dollars per unit.
    • The transcript also mentions a calculation that yields $16.33; note that if TC were $2.45, ATC would be $0.163, so the 245 figure aligns with the $16.33 result for 15 units.
  • Marginal Cost (MC): the increase in total cost from producing one more unit.
    • MC = rac{\Delta TC}{\Delta Q}
    • Example in the transcript: when production increases from zero to 10 units, the marginal cost is $8.50 (per the example), which is less than the starting point, indicating initial decreasing MC as output rises.
  • Marginal cost behavior and marginal product:
    • Rising productivity (increasing MP) tends to lower MC.
    • Falling productivity causes MC to rise.
    • MC generally rises as more workers share limited space and equipment, illustrating diminishing returns due to fixed inputs.
  • Example discussion with Jared’s factory:
    • With a small number of workers, marginal cost may be lower; after a point (e.g., more than the efficient number of workers), MC rises because adding workers yields diminishing additional output.

Short Run vs Long Run Production Decisions

  • Short run decisions:
    • Some inputs are fixed, so you decide how much to produce given fixed factors.
    • There are fixed costs that must be paid regardless of output.
    • Production decisions depend on comparing marginal cost to marginal revenue (the transcript emphasizes producing where profit is maximized, not merely increasing production).
  • Long run decisions:
    • All inputs are variable; you decide whether to invest in plant/equipment, expand capacity, or exit an industry.
    • Investment decisions depend on profitability over time.
  • Industry examples:
    • In pet rocks, low barriers to entry lead to many entrants; as supply increases, price falls, affecting profitability and encouraging some to exit or scale differently.
    • Amazon example: hiring (e.g., 5,500 in Colorado) around Black Friday in anticipation of higher demand; delivery centers and online sales underpin logistics; expansion decisions respond to expected demand peaks.

Productivity, Diminishing Returns, and Ways to Shift the Production Frontier

  • Diminishing marginal returns: as more labor is added to fixed inputs, MP initially rises and then declines; total output continues to rise but at a decreasing rate.
  • To beat diminishing returns and raise productivity across the board:
    • Training workers (improve human capital).
    • Invest in technology (capital deepening and better production processes).
    • These actions shift the production function outward, enabling higher output for the same inputs without lowering living standards.

Economic vs Accounting Costs and Profits

  • Accounting costs (explicit costs): direct monetary outlays paid by the producer (tuition, books, fees, wages, rents, etc.).
  • Economic costs: explicit costs plus implicit costs (the opportunity costs of using resources in one way rather than the next best alternative).
    • Implicit costs are not paid in money but represent the value of foregone opportunities (e.g., using own plant/equipment or time in a particular way).
    • Economic Cost = Explicit + Implicit costs.
  • Economic profit:
    • \Pi_{econ} = TR - Economic\ Cost
  • The transcript emphasizes that accounting costs capture only explicit payments, while economic costs include opportunity costs as well.
  • Divergence between accounting and economic costs occurs when a factor of production is not paid an explicit wage or rent (i.e., there are implicit costs).
  • Examples:
    • Accounting cost example: tuition, books, and fees for taking a class.
    • Economic cost example: those costs plus the value of the next best use of your time and resources (e.g., the opportunity cost of not working elsewhere or not using the resources for another project).

Dangers of Ignoring Costs and Practical Implications

  • If you hire one too many workers relative to capacity and demand, you may lose money because MC exceeds the revenue obtainable at the current output.
  • The goal remains to maximize profit, not merely to maximize production.
  • Recognize how fixed inputs (short run) constrain decisions; in the long run, invest in capacity and technology to sustain profitability.

The Malthus Reference and the Role of Technology

  • Malthus: a historical economist known as a “dismal scientist” who argued that population growth would outpace food production, leading to doom unless confronted by resource limits.
  • The lecture notes that he did not anticipate technological progress.
  • Technology and better farming practices have historically increased production and allowed living standards to rise, offsetting some of the pessimistic projections of Malthus.

Summary and Takeaways

  • Production function and capacity set the ceiling for output; beyond capacity, additional inputs do not add value.
  • Short run vs long run: fixed costs exist in the short run; all inputs variable in the long run.
  • Costs and cost curves:
    • TC = FC + VC
    • ATC = TC / Q
    • MC = ΔTC / ΔQ
  • Diminishing marginal returns imply an eventual rise in MC as output expands due to fixed inputs.
  • The profit-maximizing rule is to produce where profit is highest, balancing revenues against total economic costs (explicit + implicit).
  • Economic cost accounting requires considering opportunity costs; accounting cost only accounts for explicit payments.
  • Productivity can be increased through training and technology, shifting the production frontier outward.
  • Real-world context: firms hire and invest in capacity in anticipation of demand (e.g., Black Friday planning by Amazon).
  • Philosophical/ethical note: efficient use of resources matters for societal welfare; overstaffing and misallocation waste resources and reduce social surplus.

Key Formulas to Remember

  • Total Cost: TC = FC + VC
  • Average Total Cost: ATC = \frac{TC}{Q}
  • Marginal Cost: MC = \frac{\Delta TC}{\Delta Q}
  • Economic Cost: Economic\ Cost = Explicit\ Cost + Implicit\ Cost
  • Economic Profit: \Pi_{econ} = TR - Economic\ Cost
  • Production Function (conceptually): output as a function of inputs; diminishing returns imply MP declines with more inputs when others are fixed.
  • Marginal Product (concept): MPP = \frac{\Delta Q}{\Delta L} (change in output per additional unit of labor)