Farm Management Chapter 8: Economic Principles - Input Combinations

Chapter Outline

  • Input Combinations

Chapter Objectives

  • Substitution in Economics and Decision Making
  • Understand the concept of substitution as it relates to resource allocation and decision-making in farm management.
  • Substitution and Price Ratios
  • Learn how to compute input substitution ratios and price ratios for two given inputs.
  • Finding Least-Cost Combinations
  • Apply the input substitution and price ratios to determine the least-cost combination of two inputs for production.

Input Combinations

  • Premise: Most agricultural products require multiple inputs.
  • Management Decision: Managers must choose the optimal input combination or ratio to use.
  • Economic Consideration: Investigate if one input can substitute another to lower production costs.

Input Substitution Ratio

  • Formula:
  • Input Substitution Ratio = ΔReplaced / ΔAdded
  • This ratio measures the rate at which one input can be substituted for another.

Types of Input Substitution

  • Constant Rate of Substitution (Perfect Substitution)
  • Decreasing Rate of Substitution
  • No Substitution (implies that inputs cannot effectively replace one another)

Input Price Ratio

  • Formula:
  • Price Ratio = Price Added / Price Replaced
  • This reflects the relative costs of the inputs involved in substitution.

Decision Rule for Least-Cost Combinations

  • Establish Least-Cost Combination:
  • Set the input substitution ratio equal to the input price ratio.
  • If exact equality is not possible, choose combinations that keep the price ratio less than or equal to the substitution ratio.
  • Condition: Substitution Ratio ≥ Price Ratio

Selecting a Least-Cost Feed Ration

  • Example: Multiple feed rations with given weights and costs of grain (9¢) and hay (6¢).

Types of Substitution Outcomes

  • Constant Rate of Substitution:
  • Typically results in a complete choice of one input type, shifting to none of the other unless their ratios are equal.
  • Decreasing Rate of Substitution:
  • Usually results in a combination of both inputs being used as they are substituted for one another.

Effect of Changing Prices

  • Changes in input costs affect the least-cost combinations:
  • An increase in the price of one input generally leads to reduced usage of that input and an increased reliance on the cheaper alternative.

Summary

  • The chapter emphasizes using substitution principles to determine optimal production methods.
  • Managers identify the least-cost combinations of inputs as a strategy for effective resource management.

Exercise - Least-Cost Input Combination Calculations

  • Example Scenario:
  • Input A: $21, Input B: $3
  • Calculate the price ratio and determine the least-cost combination based on given inputs.
  • Further Scenarios:
  • If Input A costs $20 and Input B costs $8, compute the price ratio and respective least-cost combinations.

Cost Calculation for Combinations

  • To determine costs:
  • Cost = (Price of Input 1 × Amount of Input 1) + (Price of Input 2 × Amount of Input 2)
  • Example cost calculations for various combinations with specified prices of Input A and Input B.