Midterm Exam Review AAE 575 Fall 2012

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# Midterm Exam Review AAE 575 Fall 2012 - PowerPoint PPT Presentation

Midterm Exam Review AAE 575 Fall 2012. Goal Today. Quickly review topics covered so far Explain what to focus on for midterm Review content/main points as we review it. Technical Aspects of Production.

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### Midterm Exam ReviewAAE 575Fall 2012

Goal Today
• Quickly review topics covered so far
• Explain what to focus on for midterm
• Review content/main points as we review it
Technical Aspects of Production
• What is a production function? What do we mean when we write y = f(x), y = f(x1, x2), etc.?
• What properties do we want for a production function
• Level, Slope, Curvature
• (Don’t worry about input elasticity)
• Marginal product and average product
• Definition/How to calculate
• What’s the difference?
Technical Aspects of ProductionMultiple Inputs
• Three relationships discussed
• Factor-Output (1 input production function)
• Factor-Factor (isoquants)
• Scale relationship (proportional increase inputs)
• (Don’t worry about scale relationship)
• How do marginal products and average products work with multiple inputs?
• MPs and APs depend on all inputs
Factor-Factor Relationships: Isoquants
• What is an isoquant?
• Input combinations that give same output (level surface production function)
• Graphics for special cases: imperfect substitution, perfect substitution, no substitution
• How to find isoquant for a production function?
• Solve y = f(x1, x2) as x2 = g(x1, y)
Factor-Factor Relationships: Isoquants
• Isoquant slope dx2/dx1 = Marginal rate of technological substitution (MRTS)
• How calculate MRTS? Ratio of Marginal production MRTS = dx2/dx1 = –f1/f2
• Don’t worry about elasticity of factor substitution
• Don’t worry about isoclines and ridgelines
Factor Interdependence: Technical Substitution/Complementarity
• What’s the difference between input substitutability and technical substitution/complementarity?
• Input Substitutability
• Concerns substitution of inputs when output is held fixed along an isoquant
• Measured by MRTS
• Inputs must be substitutable along a “well-behaved” isoquant
• Technical Substitution/Complementarity
• Concerns interdependence of input use
• Does not hold output constant
• Measured by changes in marginal products
Factor Interdependence: Technical Substitution/Complementarity
• Indicates how increasing one input affects marginal product (productivity) of another input
• Technically Competitive: increasing x1 decreases marginal product of x2
• Technically Complementary: increasing x1 increases marginal product of x2
• Technically Independent: increasing x1 does not affect marginal product of x2
Factor Interdependence: Technical Substitution/Complementarity
• Technically Competitive f12 < 0
• Substitutes
• Technically Complementary f12> 0
• Complements
• Technically Independent f12 = 0
• Independent
What to Skip
• Returns to scale, partial input elasticity, elasticity of scale, homogeneity
• Quasi-concavity
• Input elasticity
• Elasticity of factor substitution
• Isoclines and ridgelines
Problem Set #1
• What parameter restriction on a standard production function ensure desired properties for level, slope and curvature?
• How to derive formula for MP and AP for single & multiple input production functions?
• Deriving isoquant equation and/or slope of isoquant
• Calculate cross partial derivative f12 and interpret meaning: Factor Interdependence
Production Functions
• LRP, QRP
• Negative Exponential
• Hyperbolic
• Cobb-Douglas
• Square root
• Intercept = ?
Economics of Optimal Input Use
• Basic model (1 input): p(x) = pf(x) – rx – K
• First Order Condition (FOC)
• p’(x) = 0 and solve for x
• Get pMP = r or MP = r/p
• Second Order Condition (SOC)
• p’’(x) < 0 (concavity)
• Get pf’’(x) < 0 (concave production function)
• Be able to implement this model for standard production functions
• Read discussion in notes: what it all means

Output max is where MP = 0, x = xymax

• Profit Max is where MP = r/p, x = xopt

r/p

y

x

MP

xopt

xymax

x

Economics of Optimal Input UseMultiple Inputs
• p(x1,x2) = pf(x1,x2) – r1x1 – r2x2 – K
• FOC’s: dp/dx1 = 0 and dp/dx2 = 0 and solve for pair (x1,x2)
• dp/dx = pf1(x1,x2) – r1 = 0
• dp/dy = pf2(x1,x2) – r2 = 0
• SOC’s: more complex
• f11 < 0, f22 < 0, plus f11f22 – (f12)2 > 0
• Be able to implement this model for simple production function
• Read discussion in notes: what it all means
Graphics

x2

Isoquant y = y0

-r1/r2

= -MP1/MP2

x2*

x1

x1*

Special Cases: Discrete Inputs
• Tillage system, hybrid maturity, seed treatment or not
• Hierarchical Models: production function parameters depend on other inputs: can be a mix of discrete and continuous inputs
• Problem set #2: ymax and b1 of negative exponential depending on tillage and hybrid maturity
• p(x,T,M) = pf(x,T,M) – rx – C(T) – C(M) – K
• Be able to determine optimal input use for x, T and M
• Calculate optimal continuous input (X) for each discrete input level (T and M) and associated profit, then choose discrete option with highest profit
Special Cases: Thresholds
• When to use herbicide, insecticide, fungicide, etc.
• Input used at some fixed “recommended rate”, not a continuous variable
• pno = PY(1 – lno) – G
• ptrt = PY(1 – ltrt) – Ctrt – G
• pno = PYno(1 – aN) – G
• ptrt = PYtrt(1 – aN(1 – k)) – Ctrt – G
• Set pno = ptrt and solve for NEIL = Ctrt/(PYak)
• Treat if N > NEIL, otherwise, don’t treat