Download presentation

Presentation is loading. Please wait.

Published byMaverick Weathersby Modified over 2 years ago

1
Midterm Exam Review AAE 575 Fall 2012

2
Goal Today Quickly review topics covered so far Explain what to focus on for midterm Review content/main points as we review it

3
Technical Aspects of Production What is a production function? What do we mean when we write y = f(x), y = f(x 1, x 2 ), etc.? What properties do we want for a production function – Level, Slope, Curvature – (Don‘t worry about quasi-concave) – (Don’t worry about input elasticity) Marginal product and average product – Definition/How to calculate – What’s the difference?

4
Technical Aspects of Production Multiple 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

6
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(x 1, x 2 ) as x 2 = g(x 1, y)

7
Factor-Factor Relationships: Isoquants Isoquant slope dx 2 /dx 1 = Marginal rate of technological substitution (MRTS) How calculate MRTS? Ratio of Marginal production MRTS = dx 2 /dx 1 = –f 1 /f 2 Don’t worry about elasticity of factor substitution Don’t worry about isoclines and ridgelines

8
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

9
Factor Interdependence: Technical Substitution/Complementarity Indicates how increasing one input affects marginal product (productivity) of another input Technically Competitive: increasing x 1 decreases marginal product of x 2 Technically Complementary: increasing x 1 increases marginal product of x 2 Technically Independent: increasing x 1 does not affect marginal product of x 2

10
Factor Interdependence: Technical Substitution/Complementarity Technically Competitivef 12 < 0 – Substitutes Technically Complementaryf 12 > 0 – Complements Technically Independentf 12 = 0 – Independent

11
What to Skip Returns to scale, partial input elasticity, elasticity of scale, homogeneity Quasi-concavity Input elasticity Elasticity of factor substitution Isoclines and ridgelines

12
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 f 12 and interpret meaning: Factor Interdependence

13
Production Functions Linear, Quadratic, Cubic LRP, QRP Negative Exponential Hyperbolic Cobb-Douglas Square root Intercept = ?

14
Economics of Optimal Input Use Basic model (1 input): (x) = pf(x) – rx – K First Order Condition (FOC) – ’(x) = 0 and solve for x – Get pMP = r or MP = r/p Second Order Condition (SOC) – ’’(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

15
x y MP 1)Output max is where MP = 0, x = x ymax 2)Profit Max is where MP = r/p, x = x opt r/p x x opt x ymax

16
Economics of Optimal Input Use Multiple Inputs x 1,x 2 = pf(x 1,x 2 ) – r 1 x 1 – r 2 x 2 – K FOC’s: d /dx 1 = 0 and d /dx 2 = 0 and solve for pair (x 1,x 2 ) – d /dx = pf 1 (x 1,x 2 ) – r 1 = 0 – d /dy = pf 2 (x 1,x 2 ) – r 2 = 0 SOC’s: more complex f 11 0 Be able to implement this model for simple production function Read discussion in notes: what it all means

17
Graphics x1x1 x2x2 Isoquant y = y 0 -r 1 /r 2 x1*x1* x2*x2* = -MP 1 /MP 2

18
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 – (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

19
Special Cases: Thresholds When to use herbicide, insecticide, fungicide, etc. – Input used at some fixed “recommended rate”, not a continuous variable no = PY(1 – no ) – G trt = PY(1 – trt ) – C trt – G no = PY no (1 – N) – G trt = PY trt (1 – N(1 – k)) – C trt – G Set no = trt and solve for N EIL = C trt /(PY k) Treat if N > N EIL, otherwise, don’t treat

20
Final Comments Expect a problem oriented exam Given production function – Find MP; AP; parameter restrictions to ensure level, slope, and curvature; isoquant equation Input Substitution vs Factor Interdependence – MRTS = –f 1 /f 2 vs f 12 Economic optimal input use – Single and multiple inputs (continuous) – Discrete, mixed inputs, and thresholds

Similar presentations

OK

Chapter 5 Production analysis and policy. KEY CONCEPTS production function discrete production function continuous production function returns to scale.

Chapter 5 Production analysis and policy. KEY CONCEPTS production function discrete production function continuous production function returns to scale.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on relations and functions for class 11th biology Ppt on as 14 amalgamation define Ppt on obesity and infertility Ppt on save tigers in india downloads Ppt on solid waste management in india Ppt on iis web server Ppt on waves tides and ocean currents affect Cg ppt online registration 2014 Ppt on time management training Skimming reading ppt on ipad