0b7696e6-f735-46e8-8cec-229c8bdd2ae5_Introduction_to_Agricultural_Production_Economics 2.pdf

Introduction to Agricultural Production Economics Week Week 1 Files AREC 3006 Week 1.pdf Notes not tested on quiz Lecture Notes Unit Description Application...

Introduction to Agricultural Production Economics Week Week 1 Files AREC 3006 Week 1.pdf Notes not tested on quiz Lecture Notes Unit Description Application of microeconomic principles to management decisions in agricultural production systems Methods of applied economic analysis through: production, cost and profit functions; methods for the measurement of productivity; optimisation in biological production systems; and production under risk Linear programming technique to solve decision making problems encountered by agribusiness and natural resource firms and managers in public agencies Understanding, conceptualizing, modeling and analyzing the behavior of economic actors engaged in production processes → relating this behaviour to the specifities of agricultural production processes Characteristics of Agricultural Production Agricultural output often bulky & perishable → transport and storage important Agricultural production follows biological process Production Process Transformation of factors of production into products or outputs through the use of technology Inputs: man-made/ natural, physical/ chemical/ biological inputs and labour inputs. Introduction to Agricultural Production Economics 1  Outputs: desirable (to the economy) but also undesirable (by-products/ externalities) New non-traditional outputs: offsets, credits biodiversity offset credits carbon credits carbon offsets renewable energy certificates soil health credits natural capital credits Multi and single-staged production processes Agricultural Production Types Broadacre Crops: wheat, barley, canola Horticulture: avocados, citrus, nuts Livestock: cattle, piggeries Mixed Farming:: traditional wheat/ sheep Economics of Biological Production Systems Used to make choices among: Alternative production processes or technologies Outputs or enterprise selection Resource allocation Key Issues How much and what to produce Optimal combination of resources Intertemporal allocation of resources - especially for renewable/ non renewable natural resources Producer Decisions to produce dependent on What to produce? Introduction to Agricultural Production Economics 2  How much to produce? What technology to use? What inputs and how much inputs to use? When to use the inputs? Production units (firms, farms) often called Decision Making Units Behaviour influenced by Economic surplus or profit Return on invested K and managerial skills Return on fixed factors of production - land (rent) in the case of agriculture Minimise cost of producing output (marginal, average, fixed, variable, long-run, short-run) Duality - economics decision problems viewed from production or cost side Knowledge of one implies knowledge of the other when input prices are known Also: tradition, customs, stewardship, succession planning, lifestyle Productivity and Efficiency Productivity: ratio of quantity of outputs to inputs used to produce output. Want to produce more by using less. Agriculture: reflects improvements in the efficiency with which inputs such as land, labour and capital are used to produce outputs such as crops, meat, wool and milk Growth: increase in Y beyond any associated increase in X or decrease in X for same Y → increased wellbeing! Economic progress from technological progress → lifting people out of poverty and prosperity Productivity growth measured over long term because it is treated as an indicator of technological progress - ST variability can reflect seasonal conditions Measurement through ABARES TFP - takes into account the full range of inputs and outputs that are generated on-farm World population increasing, increasing ED, increasing wealth, higher purchasing power, higher consumption, changes in diet composition and consumption levels → increased demand for processed food, meat, dairy, fish Introduction to Agricultural Production Economics 3  Efficiency: measure of how efficient a production unit is in transforming inputs into outputs (technical efficiency). There are other aspects of efficiency: allocative, economic Important for Food Security Limited supply of land, natural and environmental resources, degradation of land and other natural resources How best to allocated limited inputs while achieving optimal output sustainably - productivity to max worldwide availability of food/ or to compensate individual costs and fluctuating prices at the individual firm level ABARES Farmers TOT Index FToT index measures profitability of agriculture sector by comparing ave. price received by farmers w/ average farm costs When the FToT rises, prices received for produce increased more than farms costs (and vice-versa) Production Dynamics Time as a factor of production Fixed assets and usage over time Environmental dynamic considerations Natural resource dynamic considerations - Natural K Risk and Uncertainty In agriculture, technology is non-deterministic: i.e. 2+2 ≠ 4 exactly, but rather 2+2 = 4 + / - error. The error is due to natural factors that affect agricultural production, and could be quite large, especially on the downside. Manage with econometrics → production function estimates Input use and profit maximisation Linear programming: resource allocation w/ scarcity optimise objective function (max profit, min cost) by allocating resources (land, labour, water) to activities, subject to constraints on resources Non-linear production functions in agriculture and typically linear cost functions can be solved with optimisation methods subject to constraints - Lagrange Introduction to Agricultural Production Economics 4  Linear Programming - case of production economics optimisation which we use same general equi-marginal principle Production Economics optimisation methods - max profits by equating VMP/P≥ 1 for all inputs given constraints Review Notes What did the quick brown fox jump over? The lazy dog What colour was the fox? Brown Why was the dog lazy? So YOU won't be! Have a great semester Place a question here Place the answer here! Introduction to Agricultural Production Economics 5  Input Demand Functions, Land as Input and Land Rents Week Week 4 Notes Chapter 7, 8 and 16 Lecture Notes Determinants of quantity of variable inputs used in production Price of Inputs Cost Price of Outputs Revenue Form of Production Function Budget constraints Input Demand Function Represents derived demand for an input by a production unit prices of inputs, price of output, production function (alpha) budget constraint C x1 = x1 (py , w1 ,..., wk , α, C 0 ) For single variable input, VMP curve represents relationship b/w input price and corresponding demand for the same input - VMP curve identical to D function for input py MP P1 V MP1 = =1 w1 w1 V MP1 = w1 → py MP P1 (x1 , α) = w1 Input Demand Functions, Land as Input and Land Rents 1  relationship between quantities of input and utility/ price Algebraic Representation of Input Demand Function py MP P1 (x1 , α) = w1 means that x1 = x1 (py , w1 , α) Example: Cobb Douglas Y = f(x1 ) = Axb1 Production Vector of parameter alpha is (A,b). MP is: MPP = bAb−1 1 Input Demand Functions, Land as Input and Land Rents 2  and criterion for profit maximisation is therefore py bAxb−1 1 = w1 Isolating x1 generates the correct form 1 −1 −1 x1 = w1b−1 pyb−1 (bA) b−1 Say that alpha = [A,b]=[1,0.5] then: p2y x1 = 0.25 2 w1 which means that the demand for input falls with an increasing input price and rises with an increasing output price Input Demand Elasticity Relative change in derive demand for an input relative to the change in price (in percentages) (own price elasticity) dx/x1 dx1 w1 dlnx1 εD1 = = = dw1 /w1 dw1 x1 dlnw1 Example with Cobb Douglas: transform input demand function from CB production into log terms 1 1 1 lnx1 = lnw1 − lnpy − (lnb + lna) b−1 b−1 b−1 Elasticity - differentiate with regard to lnw_1 dlnx1 1 ϵD1 = = dlnw1 b−1 Given paramenter values, price elasticity is -2 One unit increase in input price —> 2 unit decrease in demand Output Price Elasticity dlnx1 1 εDy = =− dlnpy b−1 Input Demand Functions, Land as Input and Land Rents 3  Meaning that output price elasticity for b=0.5 is 2 Increase in price → two unit increase in output come back Multiple Inputs Substitution of Inputs Where possible, producer adjusts production along isoquant in response to change in price of an input - uses less of that input Not always possible - some inputs required in more/less fixed amount Movement along isoquant changes MPP slope of isoquant = ratio of MPP Changes in use of one input affects MP of other inputs Relationship Types Complementary - water and fertiliser - increasing i and increasing j ∂MP Pi >0 ∂xj Competitive - two different types of fertilisers, urea, ammonia - increasing i and decreasing j ∂MP Pi MR DMR If incremental units of input produce less output over time, then incremental units of output become more and more costly in terms of input requirements Y increases at decreasing rate in x, then cost must increase at increasing rate in y So, DMR implies upward sloping MC curve and upward sloping supply Optimality Optimal level of output must be in Stage II for there to be supply MR=MC above min AVC implies that price of output greater than minimum of AVC for supply MC≠ Price not related to inputs but outputs cost of producing outputs cost of inputs = MFC MC and MC of production derivative of TC wrt Y Optimisation, Costs and Duality 12  Tutorial Primal Production Problem Primal Economic Problem 1. From the primal economic problem, what is the optimal quantity of nitrogen to apply? What is the quantity of wheat that will be produced? Optimal input when VMP max - around 120 34600ish units of wheat 2. Change the price of wheat above and below 0.120 (e.g. to 0.080 and 0.160) and note how the optimal quantity of nitrogen used and wheat produced change. Increasing price of wheat means more nitrogen but unchanged optimal qunatity decreasing price results in lower optimum at 100kg/ha 3. Change the price of N above and below 2 (e.g. to 1 and 3) and note how the optimal quantity of nitrogen used and wheat produced change. Increasing price - same optimal lowered price - higher optimal 4. What happens if the price of nitrogen goes to zero? more production, basically always optimal to produce ceiling exist - wont use regardless of price as MB does not inccrease. Max at 160? Dual Production Problem Dual Economic Problem Optimisation, Costs and Duality 13  Production of Multiple Products Week Week 5 Notes Chapter 17 Lecture Notes Multiple Products/ Enterprises Farm/ agriculture often produces more than one output - beyond simple assumption Implications for the whole production model: what combinations of enterprises (outputs) should be produced from a given bundle of fixed and variable inputs optimal combination? how many for each? given what are your abilities to mobilise fixed and variable - land, rent, access to liquidity and finance Production Possibilities PPF Curve how to devote economic resources? Land and labour/ capital is fixed - can produce varying levels/ amounts Production of Multiple Products 1  Product-Product model of agrcultural production is a farm level version of PPC PPC at farm level becomes Product Transformation Curve Resource Base for the farm is a bundle of inputs that could be used to produce a combination of outputs farmer must choose to allocate available inputs between alternative outputs Optimal Choice of Enterprises Objective: determine profit maximising enterprise combinations Generally, production from one enterprise can only be increased by decreasing production from another enterprise given the limited amount of land, capital or some other input If resources are not limited, producer should produce to maximise profit in each enterprise But resources limited always No longer independent enterprises Limited Resources When amount of input is limited, optimum amount cannot be used in each enterprise - total amount of input available is less than the amount needed to optimally apply to each enterprise when inputs limited, enterprises on the arm become related and they cannot be considered independently If output of one enterprise is to be expanded, resources must be diverted to that enetrprise This means that output of other enterprises will have to be reduced Product Transformation Curve Assume one input X can produce two products Y_1 and Y_2 all other inputs are fixed cannot be diverted from a particular use Farm manager must determine how much of C to devote to production of each product (Y_1, Y_2) Production of Multiple Products 2  From one input - one output production functions to product transformation curve linear production functions —> linear production transformation non-linear production —> non-linear produxtion transformation transformation of the technology use Derivation of PTC diminishing marginal returns - more input, less can be produced marginally different rates of diminishing returns Production of Multiple Products 3  Given X=4 - can devote different amounts to each creates a production transformation curve how much to produce? depends on prices. If we don’t, we maximise quantity we can produce Different slopes of Production Transformation Curves Represent all possible co,binations of products with fixed amount of inputs but only one is optimal different PPC for each number of available inputs Mathematically PTC is inverted production curve - g describes hiw much x is used as a function of the production of y1 and y2 x = g(y1 , y2 ) Production of Multiple Products 4  Slope of transformation curve is: dy2 MP Px,y2 =− dy1 MP Px,y1 This is the Rate of Production Transformation: represents how much of y_2 must be changed if you want to produce more of y_1 but only have given amount of input x at your disposal: MP Px,y2 RP Ty1 ,y2 = − MP Px,y1 Soybean Example soybean linear, corn is non-linear calculate MPP then take ratio Relationships among products PTC illustrate relationships among enterprises on a farm relationships may take different forms depending on the situation Two outputs are normally competitive everywhere on the PT function Production of Multiple Products 5  Two outputs can only be supplementary or complementary over a portion of the transformation function Four types of relationships: Competitive: given fixed bundle x, one output must be foregone to produce more of the other under ordinary circumstances, RPTy_1,y_2 is negative When transformation function is downward sloping negative slope dy2 0 dy1 positive rate of transformation for certain combinations only complementary for the first part of the curve usually e.g. honey and fruit - bees and honey, bees increase productivity of fruit trees If unit costs of production of one output can be reduced by also producing another output, referred to as economies of scope e.g. production of livestock under conditions where disposal of manure involves considerable cost and production of crops is based on the purchase of inorganic fertiliser when combined, livestock manure used as fertiliser in crop production is cost saving Joint: Products produced in same process - fixed ratio to each other leontief - no rate of product transformation, collapse to single point which is joint single point or a right angle e.g. production of beef and hides or sheep meat and sheepskins only one hide per animal, no more orless —> transformation between beef and hides is equal to zero e.g. wool and lamb meat some sheep tend to produce more wool, others better for meat Production of Multiple Products 7  Optimal Combination of Outputs Optimisation problem in connection with a given amount of inputs consists of determining combination of outputs that results in highest total revenue R = p1 y1 + p2 y2 then derive iso-revenue (iso-income) line - all combinations that give same revenue R p1 y2 = − y1 p2 p2 first term is intercept, slope is negative ratio of price ratio - straight line iso-revenue joins combinations of two products which returns same revenue when output prices remain constant, iso revenue lines represent different total revenues which are parallel change in either price will change slope of the line isorevenue line is straight under perfect competition because output prices do not change regardless of the amount of output sold distance from origin is determined by the magnitude of total revenue isorevenue lines and cost lines look same on the graph but different revenue optimisations vs cost minimisation Show that highest R is achieved when iso-revenue line is tangent to production possibility curve Revenue Maximising Combination of Outputs total cost constant for all output combinations on PTC profits from limited resource greatest if product combination returning max total revenue is selected this will occur when the slope of the PTC cure is equal to the ratio of the prices of the products (slope of iso-revenue line) Production of Multiple Products 8  RPT of Y_1 for Y_2: dy2 MP Px,y2 p1 =− =− dy1 MP Px,y1 p2 Or ∂y2 p =− 1 ∂y1 p2 slope of PTC equals ratio of prices of products. Slope of the isorevenue curve - profit maximising combination of enterprises at point where product transformation curve is exactly tangent to the isorevenue line slopes implied to be equal Optimality condition how much input to produce in each Constrained optimisation MaxR, where R = p1 y1 + p2 y2 s.t. x = g(y1 , y2 ) Lagrange function is expressed as: L = p1 y1 + p2 y2 + λ(x − g(y1 , y2 )) Production of Multiple Products 9  Lambda is Lagrange multiplier - shadow price on the input FOC ∂g p1 − λ =0 ∂y1 ∂g p2 − λ =0 ∂y2 x − g(y1 , y2 ) = 0 Combining ∂g 1 1 1 = ∂y = ∂y = ∂y ∂g ∂x MPP p1 MP Px,y2 = p2 MP Px,y1 Can be shown that VMPy_1=VMPy_2= lambda At optimum, VMP of x in producing any output should be same and equal to shadow price of input Shadow price of input should coincide with its cost (MFC) Allocation of inputs between products can also be viewed in terms of opportunity costs it demonstrates the cost in terms of the value of an alternative product that is given up as long as the VMP in one enterprise, which is sacrificed, equals the VMP in the other enterprise, which is gained are equal: then the opportunity costs for both enterprises are equal and are given by the shadow price of the input and total returns are at a maximum if value of the marginal product given up exceeds the value of the marginal product gained: then the opportunity cost is greater than the value added and returns are below the maximum Production of Multiple Products 10  One Input - Several Products To allocate a limited amount of input among several enterprises calculate VMP for each enterprise Units of the input are allocated to each enterprise so that the marginal earnings of the input are equal in all enterprises V MPX A = V MPXB = V MPXC = V MPX n Where VMP_XA is the value of marginal product of X used on product A. If not, not at optimum General Equimarginal Principle The general equimarginal criterion states that the ratio of the value of the marginal product of an input to the unit price of the input (VMPx/Px) should be equal for all inputs in all enterprises V MPX 1Y 1 V MPX 1Y 2 V MPX 2Y 2 V MPX 1Y 2 V MPX nYn = = = =.... = PX 1 PX 1 PX 2 PX 2 PX n when the criterion is fulfilled, a dollar spent on any enterprise will have the same marginal earnings: that is, it will add the same amount to the total revenue This will only happen when we are in the competitive part of the PPC can then use same process to iterate what happens withm more input - product expansion path Production of Multiple Products 11  Multiple Production Stages Production happens in stages: the output from one stage is the input in another stage: typical in agriculture. Intermediate products Example: using grass and cereals to feed cattle. So, there are three enterprises, with grass and cereals being intermediate products, and beef being the final product. Production of Multiple Products 12  Optimisation Where the slope of the PTC is equal to slope of isoquant - slope of tangent line is the same as -pc/pg MP Px,y2 MP P1 = MP Px,y1 MP P2 this entails that the producer produces exactly the same amount that is consumed - production and consumption equilibrium. Often possible to trade intermediates - supplement production or sell the amount that cannot be used in ones own production, sell some of one input for another to increase production Production of Multiple Products 13  Productivity, Efficiency and Technological Change Week Week 6 Notes Chapter 6 + Additional Papers Lecture Notes Productivity Measure of production output relative to input use: as applied to a collection of production units, industries or sectors Ratio of quantity of outputs (or some indexes thereof) to quantities of inputs (or some indexes thereof) quantity index of outputs Productivity = quantity index of inputs Often price-weighted Interested in changes over time Interested in more than just a single production unit How productive is a sector of the economy? Within a sector? Assessment must be based on large number of production units Permanent Improvement of Productivity Increased economic wellbeing and improved quality of life Connection between factor productivity (productivity of single factor of production, e.g. labour) and its remuneration (e.g. wages) Very important to measure changes in productivity Changes in Productivity Production or output is y, input is x, then: Productivity, Efficiency and Technological Change 1  yt+1 yt xt+1 − xt Change in Productivity = dP = ( yt ) xt yt+1 xt+1 = ( yt − 1) xt yt+1 x t+1 =( − 1) yt xt Indexes Used to aggregate and weight quantities of inputs and outputs at different time periods: Output (QO) and Input (QI) indexes Laspeyre’s Index: uses based-period quantities and weights them by prices ∑(pc,tn ) ∗ (qc,t0 ) PL = ∑(pc,t0 ) ∗ (qc,t0 ) Paasche Index: uses current-period quantities and weights them by prices ∑(pc,tn ) ∗ (qc,tn ) PP = ∑(pc,t0 ) ∗ (qc,tn ) Productivity indexes: dependent on the type of weighting, there are numerous productivity indexes (Fisher, Malmquist, Tornquist…). E.g. Fisher - geometric mean of Laspeyre’s and Paasche PL ∗ Pp Total Factor Productivity Single output, multiple inputs y TFP = QI Multiple outputs, multiple inputs QO TFP = QI Multifactor productivity Productivity, Efficiency and Technological Change 2  Efficiency What is actually produced vs what could (or should) be produced given a particular technology and quantity of inputs used Relationship between efficiency and productivity: lower efficiency implies slowing down on productivity growth Efficiency: y0 f(x0 ) output dimension measurement - how much is vs what could be input dimension measurement - how much input could be saved with the same produced output quantity Efficiency Measurement Collect information on inputs used and outputs produced by many individual production units Plot these observations as x,y scatter. Each point on plot is a production unit (farm or firm) Then, draw outer ‘envelope’ of the observations using either parametric (Stochastic Production Frontier) or non-parametric (Data Envelopment Analysis) methods Envelope is also called a frontier, consists of observations on production units that produce most output for a given level of input (or use the least input for a given level of output) Production units for which the observations are on the frontier are deemed ‘efficient’ and the others are inefficient to a greater or lesser extent Productivity, Efficiency and Technological Change 3  Extent of inefficiency can be fairly accurately measured All efficiency measurements are based on measuring relative distance between given observation and frontier There are several ways that these measurements can be taken: radial or non-radial distance - measure by radial distance function directional distance - measure by directional distance function (output oriented) Productivity, Efficiency and Technological Change 4  (input oriented) several ways to form indices that will communicate the extent of inefficiency: ratios or differences Environmentally Adjusted Efficiency Measurements Ideas presented so far pertain to only ‘economic’ inputs and outputs (’desirable’ or ‘good’ outputs) However, many production processes use environmentally sensitive inputs (e.g. water, energy) and produce ‘undesirable’ or ‘bad’ outputs together with the ‘good’ output Productivity, Efficiency and Technological Change 5  If these ‘environmental’ inputs and outputs and their effects can be quantified, standard efficiency measurements can be adjusted to reflect not only economic but also environmental efficiency Typically output oriented, i.e. environmental effects from a production process, treated as ‘bad’ or ‘undesirable’ output: e.g. greenhouse gas emissions are a ‘bad’ that parallels the production of a good output (e.g. electricity, or dairy production); or degradation of environmental assets (e.g. water dependent ecosystems) as a result of producing agricultural crops or electricity Input oriented models are rarer as they are not able to identify specific environmental effects, they pertain to the use of environmentally sensitive inputs (e.g. water use) Quantifying Environmental Effects Sometimes straightforward: GHG emissions, energy use, water use, quality of treated wastewater Other times very difficult: Effects that water withdrawals have on ecological assets. How to measure them? How to establish causality relationships? How to assign values too quantities (pricing of environmental goods)? Drivers of Changes of Productivity Across Time Efficiency change: catching up lower efficiency units, and their movement towards the frontier Productivity, Efficiency and Technological Change 6  Technical/ Technological change: pushing frontier out (those production units that are on the frontier are becoming more productive over time) Productivity, Efficiency and Technological Change 7 Productivity, Efficiency and Technological Change 8  Changes in scale of production: overall increase in the scale of operations. Scale efficiency most productive at b or x1 - technically optimal scale of production Productivity, Efficiency and Technological Change 9  Production Technology, Production Functions and Profit Maximisation Week Week 2 Notes Chapter 2 and 3 Lecture Notes Production Relationships Production relationship: transformation if inputs into outputs How much should we use? How much should we not use? generally represented as the following - technology set T (x, y) = (c, y) : x can produce y Caveats More then one x and/or y which means that production technology is multi- dimensional graphical limitations partial production functions as a work around - focus on one input while assuming others are fiixed Partial representation of technology: keep other x unchanged and focus on one x Production Technology, Production Functions and Profit Maximisation 1  do not show the interactions between different inputs providing an incomplete picture of production technology Empirical observations do not necessarily reflect efficiency of technology in converting inputs into outputs. data may reflect inefficient producer Observations might be from a technically inefficient producer Input set X(y) = x : x can produce y Isoquants : G(y) = {x : x ∈ X(y) ∣ xk ∈ k / X(y) for x ≤ x} Free disposability of input also holds: the same amount of output can be produced with more input Output possibility set Y (x) = y : x can produce y Production Possibility Curve P (x) = {y : y ∈ Y (x) ∣ yk ∈ k / Y (x) for y ≥ y} Production Technology, Production Functions and Profit Maximisation 2  Free Disposability of Output Possible to produce smaller amount of y using a given level of x then what is actually being produced. If it is possible to produce 30 kg y with 10 kg x then possible to produce less – e.g. 25 kg y – with 10 kg x. Some y are not freely disposable, especially, the undesirable outputs (i.e. pollution). A producer can not get rid of those undesirable outputs at zero cost. Abatement cost Production Function Production Function: the maximum amount of Y that can be produced (through the use of a given production technology) with a given amount of X. f(x) = max{y : y ∈ Y (x)} f(x) = max{y : y ∈ T (x, y)} Functional Forms: Used in parametric methods of estimation of production functions. Are not necessary when using non-parametric methods - distance functions, linear programming Linear: Y = b0 + b1 X Quadratic 2 Production Technology, Production Functions and Profit Maximisation 3  Y = b0 + b1 X + b2 X 2 Further insights: y = a + bx + cx2 One turning point at x=-b dy = b + 2cx = 0 dx convex when c>0 and concave when c< 0, b, c > 0 and d < 0 FOC is a quadratic dy = b + 2cx + 3dx2 dx SOC d2 y = 2c + 6dx dx2 Cobb Douglas Y = Axb1 b2 1 x2 Translog Production Production Technology, Production Functions and Profit Maximisation 4  lny = lnA + b1 lnx1 + b2 lnx2 Power Functions Y = Axb Von Liebig (linear plateau function) Product Curves Production Technology, Production Functions and Profit Maximisation 5  Total Physical Product (TPP or Output): Technically possible maximum output or yield for each level of input TPP = y = f(x) Neoclassical Production Function TPP = y = a + bx + cx2 + dx3 From TPP → APP & MPP Average Physical Product (APP): Output per unit of input y f(x) APP = or x x Average rate that x is transformed into y more of variable input w/ fixed → increased productivity of variable increases then decreases Maximum APP when APP and MPP cross Marginal Physical Product (MPP): Additional output per unit of additional input dy MPP = orf ′ (x) dx Productivity of input at given point on the production function want to know effects of additional inputs Neoclassical Production Function dy MPP = = b + 2cx + 3dx2 dx Inflection point (max MPP) is where SOC=0 dMPP d2 y = 2 = 2c + 6dx = 0 dx dx −c x= 3d Marginal Returns: rate of change in Y as additional X is used - additional returns per unit of X Production Technology, Production Functions and Profit Maximisation 6  change in MPP as units of X are added to the production is equivalent to the rate of change in the TPP curve and expressed as the slope of MPP dMPP d2 y = 2 dx dx Regions of the Production Function Increasing Returns - below turning point, second derivative −c 0 3d Negative Returns are possible Law of Diminishing Marginal Returns: Adding inputs to production with at least one fixed input leads to increasing returns of output but this gradually diminishes and eventually becomes negative Assumption that DMR is a basic condition in production economics TPP and MPP MPP increasing: Y increasing at increasing rate highly elastic MPP decreasing: Y increasing at decreasing rate MPP=0, total output at maximum inelastic?? MPP negative: Y decreasing MPP and APP Vary with amount of input use Production Technology, Production Functions and Profit Maximisation 7  APP increasing: MPP>APP d(APP ) >0 dx APP constant: MPP=APP d(APP ) =0 dx APP falling: MPPAPP APP increasing and reaches max at the end of this stage never rational as APP is increasing Stage 2(Rational): E=1 when MPP=APP 0