Malthusian Trap and Production Function Notes

Administrative Announcements and Class Logistics

• Canvas Setup and Group Communication:

  • Course sections in Canvas are not yet split by section.
  • Group communication is conducted through direct email chains generated by manually selecting enrolled students.
  • Students must monitor their email regularly for all recitation announcements, guides, and materials.
  • A video guide was previously attached to an email to assist with course material and offset time constraints caused by technical issues.

• Participation and Extra Credit Policy:

  • Homework assignments completed during recitation do not need to be submitted for grading or participation points.
  • Class time is dedicated to working through homework concepts collaboratively in groups of 4 to 5 students.
  • Participation credit is awarded based on active classroom engagement and discussion rather than assignment collection.

Historical Economic Foundations: Industrial Revolution and Allen's Model

• Historical Context of the Industrial Revolution:

  • Originated in Britain during the mid-1800s before spreading globally to other developing economies.
  • Characterized by rapid technological progress, the expansion of capitalism, and exponential growth in national Gross Domestic Product ($GDP$).

• Robert Allen's Framework (High Wages and Cheap Coal):

  • Explores the economic choices made by production firms when deciding between labor costs and input technology.
  • When faced with high labor wages versus cheap technological energy sources (such as coal), profit-maximizing producers consistently select cheap coal.
  • Large producers aim to minimize expenditures on wages to maximize profits, driving technological adoption over manual labor.

The Malthusian Trap and Population Dynamics

• Mechanisms of the Malthusian Trap:

  • Technological advancement increases production and raises the standard of living, reflected in the exponential growth of $GDP$ starting in the mid-1800s.
  • Historically, higher standards of living led to increased procreation and rapid population growth.
  • Income and food resources are not distributed equally across society; resource allocation remains highly unequal while income remains concentrated.
  • When population growth outpaces accessible food and income distribution, individuals cannot obtain basic necessities and die.
  • Increased mortality forces the overall population to decline or stagnate back down to the baseline subsistence level.

• The Subsistence Cycle:

  • If population drops below the subsistence threshold, fewer people exist relative to available resources.
  • The higher resource-to-person ratio temporarily elevates the standard of living.
  • An elevated standard of living induces another cycle of population growth, pushing the population above subsistence capacity again.
  • This creates an ongoing cycle of population expansion and collapse around subsistence, a dynamic that persists in regions experiencing rapid population growth without equitable resource distribution.

Malthusian Production Function: Core Assumptions

• Assumption 1: Diminishing Average Product of Labor:

  • Graphically illustrated as an increasing concave curve (concave down).
  • The horizontal axis ($x$) represents population size or labor input (e.g., number of people).
  • The vertical axis ($y$) represents total output produced.
  • Total production increases as additional labor is added, but it increases at a decreasing rate, causing the curve to flatten.
  • Analogy of "Too Many Cooks in the Kitchen":
  • Consider a scenario of living in a small house with 5 roommates.
  • If one person enters the small kitchen to prepare meals, productivity is high.
  • If all 5 roommates enter the same small kitchen simultaneously to cook, overcrowding occurs.
  • Additional people in a fixed space cause tasks to take longer, reducing individual and average productivity relative to 1 or 2 workers.

• Assumption 2: Population Growth Above Subsistence:

  • Population size expands whenever the average product of labor exceeds the subsistence level required for survival.
  • When output generates a surplus beyond survival needs, population increases.
  • Population growth continues until average product drops back to or below subsistence, curbing further growth.

Practical Application: Homework 1.2 and Exam Guidance

• Homework 1.2 Setup:

  • Located under the Week 2 module on Canvas.
  • Evaluates a agricultural community where grain harvest totals depend on the number of farmers working within a shared space.
  • Variable Definitions:
  • Total product ($y$): Total bushels of grain harvested per week.
  • Input ($x$): Number of active farmers working in the shared land area.
  • Analysis relies directly on evaluating the provided production function equation rather than using a logistic growth model.

• Computation and Exam Requirements:

  • Homework calculations can be computed by hand or using spreadsheet software such as Microsoft Excel or Google Sheets.
  • Performing calculations manually by hand is strongly encouraged for exam preparation.
  • Exam questions will require students to manually compute and complete numerical tables using a given production function without software tools.