AAEC 2305 Fundamentals of Ag Economics CHAPTER 3 Production Functions and Product Curves

Factors of Production b Inputs are generally designated as “X” 1) Fixed Inputs - factors must be maintained (i.e. paid for, kept up, etc.) whether pdn occurs or not (ex. - land, buildings, heavy machinery, etc.)1) Fixed Inputs - factors must be maintained (i.e. paid for, kept up, etc.) whether pdn occurs or not (ex. - land, buildings, heavy machinery, etc.) 2) Variable inputs - factors that vary as the output level changes (ex. - labor, fertilizer, seed, etc.)2) Variable inputs - factors that vary as the output level changes (ex. - labor, fertilizer, seed, etc.)

Short vs. Long Run b 1) Immediate Short-Run: Time span so short that no resource changes can be made. All factors of pdn are fixed. b 2) Short-Run: Time span such that some factors are variable & some factors are fixed. b 3) Long-Run: Time span so long that no inputs are fixed.

Production Function (PF) b Defn: The technical relationship between inputs & output indicating the maximum amount of output that can be produced using alternative amounts of variable inputs in combination with one or more fixed inputs under a given state of technology. b Or, simply speaking, it is the technical relationship between inputs & output

Product Curves b Used to study PF b Total Physical Product (TPP) - illustrates relationship that exists between output and one variable input, ceterus paribus Indicates total amount of output produced at each level of input useIndicates total amount of output produced at each level of input use

Product Curves (Cont.) b Average Physical Product (APP) - shows how much pdn, on average, can be obtained per unit of the variable input with a fixed amount of other inputs Indicates avg productivity of the inputs being used - how productive is each input level on averageIndicates avg productivity of the inputs being used - how productive is each input level on average APP = TPP / X APP = TPP / X

Product Curves (Cont.) b Marginal Physical Product (MPP) - represents the amount of additional (i.e., marginal) TPP obtained from using an additional unit of variable input (X). The slope of the TPP curveThe slope of the TPP curve We use the MPP to identify the rate of change in output resulting from adding one more unit of inputWe use the MPP to identify the rate of change in output resulting from adding one more unit of input MPP = ΔTPP / ΔXMPP = ΔTPP / ΔX

Law of Diminishing Marginal Physical Product b Law of Diminishing Marginal Physical Product: As additional units of one input are combined with a fixed amount of other inputs, a point is always reached where the additional product received from the last unit of added input will decline

Relationships between Product Curves b MPP is slope of TPP b At Inflection Point (pt of diminishing mpp): TPP Δ’s from increasing at an increasing rate to increasing at a decreasing rateTPP Δ’s from increasing at an increasing rate to increasing at a decreasing rate Therefore, MPP reaches a maximum at inflection pointTherefore, MPP reaches a maximum at inflection point

Relationships between Product Curves b MPP = 0 occurs when TPP is maximum b MPP is negative beyond TPP max b

Relationships between Product Curves b APP measures the average productivity of each unit of variable input being used Drawing a line from the origin which is tangent to the TPP curve gives APP maxDrawing a line from the origin which is tangent to the TPP curve gives APP max At point where APP is max, MPP crosses APP (MPP=APP)At point where APP is max, MPP crosses APP (MPP=APP)

Summary of Relationships b When MPP > APP, APP is increasing b When MPP = APP, APP is at a max b When MPP < APP, APP is decreasing b The relationship between TPP, APP, & MPP is very specific. If we have COMPLETE information about one curve, the other two curves can be derived.

Stages of Production: Rational & Irrational b In stage I: TPP is increasingTPP is increasing APP is increasingAPP is increasing MPP increases, reaches a maximum & decreases to APPMPP increases, reaches a maximum & decreases to APP IRRATIONAL STAGE BECAUSE APP IS STILL INCREASINGIRRATIONAL STAGE BECAUSE APP IS STILL INCREASING

Stages of Production: Rational & Irrational b In Stage II: TPP is increasingTPP is increasing APP is decreasingAPP is decreasing MPP is decreasing and less than APP, but still positiveMPP is decreasing and less than APP, but still positive RATIONAL STAGE BECAUSE TPP IS STILL INCREASINGRATIONAL STAGE BECAUSE TPP IS STILL INCREASING

Stages of Production: Rational & Irrational b In Stage III: TPP is decreasingTPP is decreasing APP is decreasingAPP is decreasing MPP is decreasing and negativeMPP is decreasing and negative IRRATIONAL STAGE BECAUSE TPP IS DECREASINGIRRATIONAL STAGE BECAUSE TPP IS DECREASING

Stage II of Production b Note: For each additional unit of X that is being used within stage II, TPP is increasing but APP is decreasing, resulting in a trade-off between increased production & decreased productivity for each input. This trade-off is the core of economic decision making and requires the skills of the decision maker.

Effects of Technological Change b We know that the PF gives the max amount of output that can be produced by a firm using a given technology. b The PF can shift over time as a result of a technological change

Effects of Technological Change b Technological change refers to the introduction of new technology that increases output with the same amount of resources (i.e., the TPP curve would shift upward) b The technological change that shifts the TPP upward would result in a corresponding upward shift in the APP & MPP curves