Outline Preconditions Competences: What are you supposed to learn? The framework and definition of herd management The management cycle Objectives of production, utility theory Advanced Herd Management Classical production theory Course introduction Classical replacement theory Limitation of classical theories Anders Ringgaard Kristensen Outline of the course Teachers The concept of uncertainty Slide 1 Slide 2 Preconditions Preconditions UR 2005 Courses • ”Husdyrproduktion” Not all of you have had a chance to fulfill the preconditions • ”Matematik og modeller”/”Matematik og defined in UR 2005. planlægning” My guess is that very few have had those courses. As a consequence of this assumption, the course will start • ”Statistisk dataanalyse 2” up with a brush-up course of • Mandatory first year (economics etc) • Probability calculus and statistics • Linear algebra Slide 3 Slide 4 Competencies I Competencies II Competencies obtained within basic science: • Comprehension of advanced methods for Competencies obtained within applied science: production monitoring and analysis as well as operational and tactical planning in livestock • Apply principles and advanced methods for production herds. monitoring based on data from specific herds. • Apply principles and advanced methods for operational and • Evaluation of various methods in relation to the tactical planning in specific livestock herds. solution of typical management problems in • Apply principles and advanced methods in development of livestock herds. general herd management tools. • Make judgements concerning the choice of • Make judgements concerning the quality of commercially appropriate methods for different herd distributed general herd management tools. management tasks. Competencies obtained within Ethics & Values: • Is aware of the relation between monitored production traits and the priorities defined by the farmer’s utility function. Slide 5 Slide 6 1
A pig (an animal) Pig production = N × a pig? Medicine Medicine Piglets Piglets Meat Meat Manure Manure Feed Feed Milk Milk Slide 7 Slide 8 Pig production Pig production = N × a pig? Pigs: •Ages •Groups •Individuals Medicine Buildings Fields Neighbors, society, consumers Piglets Meat Manure Feed Milk Owner Farm hands Feed Slide 9 Slide 10 Elements of production I Elements of production II The factors (input to production) Objectives: Maximization of the farmer’s welfare: • Animals • Income (personal) • Feed • Leisure time (personal) • Buildings, inventory • Labor • Animal welfare (animals) • Management • Working conditions (farm hands) • Veterinary services • Environmental preservation (future generations) • Energy • … • Prestige (personal) • Product quality (consumers) Slide 11 Slide 12 2
Elements of production III Definition of herd management Constraints limiting production Having discussed the three key elements: • Factors (input to production) • Physical (land, housing capacity, storage capacity) • Objectives (farmer’s welfare) • Economical (capital, prices) • Constraints (limitations) • Legal (laws) we are now able to define what we mean by Herd • Personal (skills, education) Management: Herd management is a discipline serving the purpose of concurrently ensuring that the factors are combined in such a way that the welfare of the individual farmer is maximized subject to the constraints imposed on his production. A dynamic optimization problem under constraints. Decisions! We decide how to combine the factors. Slide 13 Slide 14 The management cycle: Classical theories The management cycle: A never ending story (Scarce Utility Resources) Theory, Ch. 3. Basic Neo-classical Production Production Monitoring, Theory, Ch. 5. Ch. 4. (Animal science, Production function) Slide 15 Slide 16 Herd Management Science Utility theory We need a criterion for Basic level: comparison of plans • As we define the basic level, it consists of (“ways” to produce). • Utility theory Several concerns: Animals • Neo-classical production theory • The farmer • Basic production monitoring • The staff • (Animal nutrition, animal breeding, ethology, • Consumers Farm buildings Land Neighbors, society, consumers farm buildings) • The animals • What any animal scientist should know about • Environment management • … • The starting level of this course Who decides the weighting? Owner Farm hands Slide 6 Feed • Briefly revised today My answer: The farmer! Slide 17 Slide 18 3
Farmer’s preferences When is ”something” an attribute? The farmer has/defines a list of concerns: When it directly influences the subjective welfare of the farmer. • Own direct concerns: • Income, u 1 May NOT be an attribute: • Leisure time, u 2 • Average milk yield of cows • Prestige, u 3 • Average daily gain of slaughter pigs • ... • Animal welfare, ”because animals at a high level of welfare also produce at a higher level”. • Indirect concerns (because he cares for others) • Animal welfare, u 4 May be an attribute: • Working conditions, u 5 • Monetary gain • Leisure time • Environment, u 6 • Animal welfare, if the farmer is willing to accept that • Product quality, u 7 it to some extent decreases the levels of other • … attributes. The farmer knows/decides the weighting The “items” on the list ( u 1 , u 2 , … , u k ) are called attributes of the farmer’s utility. Slide 19 Slide 20 Aggregation of attributes: Utility function Consequences measured by attributes Stage The utility function Attribute 1 2 … T • Aggregation over time • Monetary gain 1 u 11 u 12 … u 1 T • Animal welfare 2 u 11 u 22 … u 2 T • … • Aggregation over attributes … … … … … k u 11 u k2 … u kT At any stage, the attributes will depend on the production Y t and Expected Utility Theorem: Maximization of U is all we need the factors x t . The relation is given by the attribute function h: to care about! Refer to Chapter 3 for details! u t = h( Y t , x t ) Slide 21 Slide 22 Production function Production function In classical production theory, the uncertainty represented by the e’s is ignored. Slide 23 Slide 24 4
Neo-classical production theory What to produce Answers 3 basic questions: Two products y 1 and y 2 • What to produce. Prices p 1 and p 2 . • How to produce. Fixed factor allotment • How much to produce. Value of production: u = p 1 y 1 + p 2 y 2 Marginal considerations Fixed value u’: Basic principle: Continue as long as the • y 2 = u’/p 2 – ( p 1 /p 2 ) y 1 marginal revenue, MR, exceeds marginal costs, MC. At optimum we have MR = MC. The price ratio p 1 / p 2 determines the optimal combination! The general principle: Continue producing one more unit of Product 1 (reducing the output of Product 2 accordingly) as long as the marginal revenue exceeds the marginal costs. Slide 25 Slide 26 What to produce: Two products How to produce y 2 Two factors x 1 and x 2 Prices p 1 and p 2 . p 1 / p 2 = 2 Fixed production Cost of production: c = p 1 x 1 + p 2 x 2 Fixed value c’: • x 2 = c’/p 2 – ( p 1 /p 2 ) x 1 The price ratio p 1 / p 2 determines the optimal combination! The general principle: Continue adding one more p 1 / p 2 = 1/2 unit of Factor 1 (reducing the output of Factor 2 accordingly) as long as the marginal revenue exceeds the marginal costs. y 1 Slide 27 Slide 28 How to produce: Two factors How much to produce x 2 One factor x and one product y Prices p x and p y A production function y = f( x ). Profit u ( x ) = yp y – xp x = f(x) p y – xp x Problem: • Find the factor level that maximizes the profit 0 x 1 Slide 29 Slide 30 5
How much to produce How much to produce Maximum profit where u’ ( x ) = 0. u ( x ) = f(x) p y – xp x 1 Total revenue, f( x ) p y u’ ( x ) = f’( x ) p y – p x 0 ,8 u’ ( x ) = 0 ⇔ f’( x ) p y = p x 0 ,6 Maximum profit where: 0 ,4 • Marginal revenue = Marginal Average revenue, f( x ) p y / x 0 ,2 cost! 0 Marginal revenue, f’( x ) p y -0 ,2 Slide 31 Slide 32 How much to produce, optimum How much to produce, logical bounds 1 1 Total revenue, f( x ) p y Total revenue, f( x ) p y 0 ,8 0 ,8 0 ,6 0 ,6 0 ,4 0 ,4 Average revenue, f( x ) p y / x Average revenue, f( x ) p y / x 0 ,2 0 ,2 Price of factor p x 0 0 Marginal revenue, f’( x ) p y Marginal revenue, f’( x ) p y -0 ,2 -0 ,2 Slide 33 Slide 34 Classical replacement theory Definition Replacement: • When an existing asset is substituted by a new The replacement problem in a broad sense is one of the most one with (more or less) the same function. important decision problems in animal production. • Examples: Dynamics: What we decide at this stage (keep/replace) may • Light bulbs influence production in many future stages. • Cars Many other decision problems relate to the replacement • Sows problem: • Milking robots • Insemination • Treatment for diseases • Feeding level • … A correct handling of the other problems implies that the question of replacement must be taken into account. Slide 35 Slide 36 6
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