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.