AREC2001: Economics of Biological Production Systems

Transcription

1 1

2 AREC2001: Economics of Biological Production Systems ONE INPUT/ ONE OUTPUT Definitions 1. Production: process of combining and coordinating two or more materials to produce output 2. Production Function: a relationship between the maximal technically feasible output and the inputs needed to produce that output which is technologically efficient a. PF analyse changes in output respective to changes in variable inputs when combined with fixed 3. Production Technology: 4. Intertemporal Choice: decisions made in one period, and how that may influence possibilities available in a subsequent period. 5. Variable Inputs: all factors are variable in the long run, but some may be fixed in the short run 6. Endogenous Variables: solution value is a product of the model 7. Exogenous Variable: value is determined by outside variables of the model à value is not accounted for/ explained by the model (Note: tend to assume technology is constant or exogenously specified) 8. Necessary Condition: prevents the event/ outcome 9. Sufficient Condition: ensures the event 10. Comparative Static Analysis: analyzing the impact upon a dependent (endogenous) variable when some exogenous shock occurs à comparison of different equilibrium states associated with different sets of values of parameters and exogenous variables Production Functions Interaction terms: situation where two inputs are determinants of production, and the two interact to determine the yield Y = b 0 + b 1 N + b 2 N 2 + b 3 NW Linear Quadratic Cubic Y = b 0 + b 1 X Y = b 0 + b 1 N + b 2 X 2 Y = b 0 + b 1 N + b 2 X 2 + b 3 X 3 Transcendental - Example is exponential or logarithmic function and is basis of more complicated growth models - Translogs are not algebraic functions à relationship that can not be accounted for with algebra Y = b 0 exp(b 1 X) Cobb-Douglas Y = a 1 X 1 b1 X 2 b2 Linear Form: logy = loga + b 1 logx 1 +b 2 logx 2 Y=AL β K α - Alpha and Beta are the output elasticity s of capital and labour (determined by available technology) - Output elasticity measure the responsiveness of output to a change in levels of either labour or capital used in production o If α =0.45, a 1% increase in capital usage would lead to approx. 0.45% increase in output - If α + β = 1, the production function = CRS - If α + β < 1, the production function = DRS - If α + β > 1, the production function = IRS Cobb Douglas will only exemplify one of the above three regions. 2

3 Elasticity of Production (EP) So: - Concerned with changes in single factor is varied and all others held constant - Calculates the % changes in output from a 1% change in input - Stage 2 is the recognized stage for optimal production and where EP = 1 (MP=AP) - EP is non-constant à it varies with the amount of input used in production, implying a non-constant ratio of MP to AP for all levels of x EP > 1 when MP > AP EP = 1 when MP = AP 0 < EP < 1 when 0 < MP < AP EP < 0 when MP < =0 < AP EP for Neo-classical Production Function EP for Cobb Douglas Function Elasticity of production in Cobb Douglas Functions are constant at coefficient b à output is always changing by the same percentage amount irrespective to stage of production where change is taking place à if analysis is done using power function, this would constitute a maintained hypothesis. Costs (Dual) COST ACRONYM DESCRIPTION Only exist in the short run where FC must be paid regardless of the amount of output produced. Examples of Cash FC: Fixed Cost FC o Rates, land taxes, insurance premiums o Principal + Interest Examples of Non-Cash FC: o Depreciation Total cost of output produced depends on amount of inputs needed to produce the output Shape of TVC curve is closely linked to the production function Total Variable Cost TVC Calculated by multiplying the amount of variable input used by the price per unit of input o TVC = shape of production function VC = Px.X AVC = TVC/Y which is same as PxX/Y which is same as Px/AP AVC varies depending on the amount of production Include costs of fuel, seed, fertiliser, chemical etc Average Variable AVC Cost AVC is inversely related to APP Refer to Stages o When APP is increasing, AVC is decreasing o When APP is at a maximum, AVC is at a minimum o When APP decreasing, AVC is increasing Marginal Cost MC Value of the incremental unit of output from additional unit of input MC = dtvc/dy MC = Px(dx/dy) Px/MP 3

4 Substitution - Problem is in the determination of whether more of one input can be substituted for less of another, thereby reducing total input cost - In the factor-product relationship, given level of output can be produced in only one way however when two or more inputs are variable, a given amount of output can be produced in more than one way. - This creates the factor factor relationship where each input has its own production function, and when used together, the production function is: - MPP must be positive for input substitution to be feasible.. - Substitution depends on the technical relationship between inputs (not economic). o Technical relationship refers to the effect one input has on the marginal productivity of the other input Isoquants - Factor-factor relationships permit a given amount of output to be produced with different combinations of inputs o Inputs substitute for each other in different proportions depending on the amount of each being used - Curve joining all combinations of X 1 and X 2 that produce a given output level is referred to as an isoquant Substitutes - Definition 1: inputs are substitutes if you can COMPLETELY REPLACE on input with the other and still produce the same output - Definition 2: inputs are substitutes if you can at least PARTIALLY REPLACE one input with the other and still produce the same level of output. Three Types Of Relationships Possible Between Inputs 1. Technical Complements, e.g. L and K, fertiliser and water o Have a synergistic impact on output o Production function with a positive interaction term (either inherently multiplicative or additive with interaction term) o Note: inputs that are technical compliments can still substitute for each other along a downward sloping isoquant line 2. Technically Competitive (Substitutes), e.g. rainfall and irrigation, bad team o Have an adverse (antagonistic) impact on output o Production function with a negative interaction term (either inherently multiplicative or additive with interaction term) 3. Technically Independent o Implies inputs have an additive impact on output only o Production function with no interaction term (inherently additive) NOTE: - Notice that the interdependency between the two inputs will determine the level of curvature of isoquants, and thus will determine the rate at which the factors substitute for each other. - Inherently additive production functions require one input to produce output. Boundary solutions are possible. Isoquants intersect both axes - Inherently multiplicative production functions require both inputs to produce output. Only internal solutions are possible. Isoquants become asymptotic (limiting factor) to both axes. Types of substitution 1. Constant rate of substitution a. Perfect substitutes b. Isoquants have linear relationship c. Corner solutions are possible (can produce output using only one input) 2. Decreasing input substitution a. Input being increased substitutes for successively smaller amounts of input being replaced 3. No substitution (inputs are compliments) 4

5 a. Inputs must be used in fixed proportions b. Isoquant is right angled substitution between inputs not feasible Equation of Isoquant - Fixed level of output/production Y0. Therefore the total revenue for each isoquant is also fixed - Isoquant equation defines level of one input needed to get specified amount of output as a function of the other input - Each level of an input no longer produces a unique level of output PRODUCTION WITH MULTIPLE INPUTS/ TWO OUTPUTS Production Possibility Curve Represents the possible alternative efficient sets of outputs from a given set of resources. For enterprises, PPC are used to determine the most profitable combination of enterprises for a limited amount of input. Also referred to as Isoresource Curves. Production Possibilities at Farm Level vs Firm Level - Product-product model of ag production is a firm level version of the PPC à resource base for the farm I a bundle of inputs that could be used to produce either of two outputs - PPC at firm level known as production transformation curve (PTC) à firm owners can rely on the market to provide an indication of the proportions of the input bundle that should be allocated to each alternative use - To determine profit maximising enterprise combinations, must first determine physical relationship among the enterprises given its constraints (land/ capital/ some other inputs) Limited/ Unlimited Resources - When input available is unlimited, should be allocated by MVP x = P x - When input available is limited, should be allocated by MVP x = P x o Enterprises at farm level become uniquely related when resources are limited à when output of one expands, resources must be diverted and output of others will be reduced Why is the curve concave to 0,0? subject to diminishing returns. Greatest yields result when the farmer allocates all of the input bundle to the production of one of the possible inputs but then non of the alternative output is produced. Three Types Of Relationships Possible Between Enterprises 1. Complementary Products, e.g. legumes in rotation with cereal crops and wheat production and land left fallow à both will increase wheat yield 5

6 - Have a synergistic relationship: when production of y1 causes the output of y2 to increase - dy 2 /dy 1 > 0 - Enterprises will generally be complimentary for a limited part of the curve before becoming competitive à THUS the profit maximizing combination of complimentary enterprises will not be within the complementary range (will be at least the point where the relationship changes) 2. Competitive Products (Substitutes) - One output must be forgone in order to produce additional of the other output à RPTy1y2 will be negative - Product Transformation Function downward sloping - dy2/dy1 < 0 3. Supplementary Products - An output y1 is supplementary if increases to output y1 is possible without any reduction in y2 output. - Either zero or infinite rate of Production Transformation Function 4. Joint Products e.g production of wool and lamb - Products that are produced in the same production process - Must be produced in fixed ratio with each other - PTF either single point or right angle ASSIGNMENT PREP Wheat MPP, APP Wheat Output vs Nitrogen Wheat (t/ha) Nitrogen (kg/ha) TPP Stage I to Stage II Stage II to Stage III MPP, APP (physical units) Nitrogen (kg/ha) MPP APP Stage I to Stage II How can you determine the quantity of nitrogen that maximizes TR minus TVC? TR TVC = profit. Thus, the level of nitrogen that maximized profit is the level associated with the point where the gap between TR and TVC is the largest. Since FC are constant, this is the same point corresponding to the max of TR-TC. How can you determine the optimal quantity of nitrogen from the VMP, VAP and MIC chart? Optimal quantity of nitrogen can be found at the intersection of VMP=MIC where the cost of the last unit produced is just covered by its revenue (necessary condition). This can also be found where VMP = P n. Optimality can only occur in the rational stage of production. To apply this rule, the intersection of VMP and MIC must occur when VMP is decreasing (sufficient condition) such that value marginal cost is less than value average cost. Do fixed costs have an impact on the graph? Fixed Costs must be paid irrespective of output and therefore completely independent from the level of production. Their only graphical impact is to shift the TC curve higher by the amount of the fixed cost. Since only Marginal and Average values are included in this graph, they have no impact. 6