Production

       Lecture 7. Production

1. The process of production and it’s objective
2. Production Function
3. Time and Production. Production in the Short-Run

3.1. Average, Marginal and Total Product

     3.2. Law of diminishing returns

       4. Producer’s behavior

            4.1. Isoquant and Isocost

            4.2. Cost minimization (Producer’s choice optimisation) 

1. The process of production and it’s objective

       Production is the process of altering resources or inputs so they satisfy more wants. Before goods can be distributed or sold, they must be produced. Production, more specifically, the technology used in the production of a good (or service) and the prices of the inputs determine the cost of production. Within the market model, production and costs of production are reflected in the supply function.

       Production processes increase the ability of inputs (resources) to satisfy wants by:

       – a change in physical characteristics;

       – a change in location;

       – a change in time;

       – a change in ownership.

       At its most simplistic level, the economy is a social process that allocates relatively scarce resources to satisfy relatively unlimited wants. To achieve this objective, inputs or resources must be allocated to those uses that have the greatest value. In a market setting, this is achieved by buyers (consumers) and sellers (producers) interacting:

       As we know consumers or buyers wish to maximize their utility or satisfaction given (or constrained by) their incomes, preferences and the prices of the goods they may buy. The behavior of the buyers or consumers is expressed in the demand function.

       The producers and/or sellers have other objectives. Profits may be either an objective or constraint. As an objective, a producer may seek to maximize profits or minimize cost per unit. As a constraint the agent may desire to maximize “efficiency” market share, rate of growth or some other objective constrained by some “acceptable” level of profits.

       All firms must make several basic decisions to achieve what we assume to be their primary objective – maximum profits:

1. How much output to supply;
2. Which production technology to use;
3. How much of each input to demand.

       In the long run, a private producer will probably find it necessary to produce an output that can be sold for more than it costs to produce. The costs of production (Total Cost, TC) must be less than the revenues (Total Revenue, TR).

    So the behavior of profit-maximizing firms can be described with the following scheme called “Determining the optimal method of production”: 
 

    

       In the circular flow diagram found in most principles of economics texts, production takes place in a "firm" or "business." When considering the production-cost relationships it is important to distinguish between such production units as firms and plants.

       A plant is a physical unit of production. The plant is characterized by physical units of inputs, such as land (R) or capital (K). This includes acres of land, deposits of minerals, buildings, machinery, roads, wells, and the like.

       The firm is an organization that may or may not have physical facilities and engage in production of economic goods. In some cases the firm may manage a single plant. In other instances, a firm may have many plants or no plant at all.

       The cost functions that are associated with a single plant are significantly different from those that are associated with a firm. A single plant may experience economies in one range of output and diseconomies of scale in another. Alternatively, a firm may build a series of plants to achieve constant or even increasing returns. General Motors Corp. is often used as an example of an early firm that used decentralization to avoid rising costs per unit of output in a single plant.

       Unless specifically identified, the production and cost relationships will represent a single plant with a single product.  

       2. Production Function

       A production function is a model (usually mathematical) that relates possible levels of physical outputs to various sets of inputs. It shows the maximum amount of the good that can be produced using alternative combinations of capital (K) and labor (L):

       Q = f (L, K, technology, ...).

       Here we will use a Cobb-Douglas production function that usually takes the form: Q = AL^a K^b

       Talking about production function it is important to note that it shows as well the production technology which means the quantitative relationship between inputs and outputs. There are two kinds of technologies:

       Labor-intensive technology relies heavily on human labor instead of capital.

       Capital-intensive technology relies heavily on capital instead of human labor.

       And to find out which is more effective we use such terms as:

       1) Technical efficiency defined as a ratio of output to input:

       Efficiency Technical =  Output/ Input

       2) Economical efficiency defined as a ratio of value of output to value of input:

       Efficiency Economical =  Output value / Input value

       In this simplified version, each production function or process is limited to increasing, constant or decreasing returns to scale over the range of production. In more complex production processes, "economies of scale" (increasing returns) may initially occur. As the plant becomes larger (a larger fixed input in each successive short-run period), constant returns may be expected. Eventually, decreasing returns or "diseconomies of scale" may be expected when the plant size (fixed input) becomes "too large." This more complex production function is characterized by a long run average cost (cost per unit of output) that at first declines (increasing returns), then is horizontal (constant returns) and then rises (decreasing returns).

       This production function can exhibit any returns to scale:

       f(mK,mL) = A(mK)^a(mL) ^b = Am^a+b K^aL^b = m ^a+b f(K,L)

       – if a + b = 1 – constant returns to scale

       – if a + b > 1 – increasing returns to scale

       – if a + b < 1 – decreasing returns to scale 

       3. Time and Production. Production in the Short-Run

       As the period of time is changed, producers have more opportunities to alter inputs and technology. Generally, four time periods are used in the analysis of production:

    "Market period" – a period of time in which the producer cannot change any inputs nor technology can be altered. Even output (Q) is fixed.

    "Short-run" – a period in which technology is constant, at least one input is fixed and at least one input is variable.

    "Long-run" – a period in which all inputs are variable but technology is constant.

    "The very Long-run" – during the very long-run, all inputs and technology change.

       Cost analysis in accounting, finance and economics is either long run or short-run.  

       3.1. Average, Marginal and Total Product

       In the short-run, at least one input is fixed and technology is unchanged during the period. The fixed input(s) may be used to refer to the "size of a plant." Here K is used to represent capital as the fixed input. The relationship between the variable input (here L is used for "labour") and the output (Q) can be viewed from several perspectives.

       The short-run production function will take the form Q = f (L), K and technology are fixed or held constant A change in any of the fixed inputs or technology will alter the short-run production function.

       In the short run, the relationship between the physical inputs and output can be describes from several perspectives. The relationship can be described as the total product, the output per unit of input (the average product, AP) or the change in output that is attributable to a change in the variable input (the marginal product, MP).

       Total product (TP or Q) is the total output. Q or TP = f(L) given a fixed size of plant and technology.

       Average product (APL) is the output per unit of input. AP = TP/L (in this case the output per worker). APL is the average product of labour.

       Marginal product (MPL) is the change in output "caused" by a change in the variable input (L), so MPL = ∆Q/∆L.

       Over the range of inputs there are four possible relationships between Q and L

    1) TP or Q can increase at an increasing rate. MP will increase, (In Figure this range is from O to L_A.)

   2) TP may pass through an inflection point, in which case MP will be a maximum. (In Figure, this is point A at L_A amount of input) TP may increase at a constant rate over some range of output. In this case, MP will remain constant in this range.

   3) TP might increase at a decreasing rate. This will cause MP to fall. This is referred to as "diminishing MP." In Figure, this is shown in the range from L_A to L_B.

   4) If "too many" units of the variable input are added to the fixed input, TP can decrease, in which case MP will be negative. Any addition of L beyond L_B will reduce output; the MP of the input will be negative. It would be foolish to continue adding an input (even if it were "free") when the MP is negative.

       The average product (AP) is related to both the TP and MP. Construct a ray (OR in Figure) from the origin to a tangent point (H) on the TP. This will locate the level of input where the AP is a maximum, LH. Note that at LH level of input, APL is a maximum and is equal to the MPL. When the MP is greater than the AP, MP "pulls" AP up. When MP is less than AP, it "pulls" AP down. MP  will always intersect the AP at the maximum of the AP.

       3.2. Law of diminishing returns

       Law of diminishing returns means that as the level of a variable input rises in a production process in which other inputs are fixed, output ultimately increases by progressively smaller increments. The law of diminishing marginal product says that if we keep increasing the employment of an input, with other inputs fixed, eventually a point will be reached after which the resulting addition to output (i.e., marginal product of that input) will start falling.

       A somewhat related concept with the law of diminishing marginal product is the law of variable proportions. It says that the marginal product of a factor input initially rises with its employment level. But after reaching a certain level of employment, it starts falling.

       The reason behind the law of diminishing returns or the law of variable proportion is the following. As we hold one factor input fixed and keep increasing the other, the factor proportions change. Initially, as we increase the amount of the variable input, the factor proportions become more and more suitable for the production and marginal product increases. But after a certain level of employment, the production process becomes too crowded with the variable input and the factor proportions become less and less suitable for the production. 
 
 

       4. Producer’s behavior

       4.1. Isoquant and Isocost

       Isoquant is just an alternative way of representing the production function. Consider a production function with two inputs factor 1 and factor 2. An isoquant is the set of all possible combinations of the two inputs that yield the same maximum possible level of output. Each isoquant represents a particular level of output and is labelled with that amount of output.      Cobb-Douglas Isoquants

        An isoquant plots all the combinations of two inputs that will produce a given output level. A point on the isoquant curve is technically efficient.

       In general, isoquants are downward sloping – the more labor we use, the less capital we need. It is bowed inward because of the law of diminishing marginal productivity. In the case of Cobb-Douglas Isoquants inputs are not perfectly substitutable.

       The slope of an isoquant shows the rate at which L can be substituted for K.

       - slope = marginal rate of technical substitution (MRTS). RTS > 0 and is diminishing for increasing inputs of labor. The marginal rate of technical substitution (RTS) shows the rate at which labor can be substituted for capital while holding output constant along an isoquant:

       

or 

       Isoquant map – a set of isoquant curves that show technically efficient combinations of inputs that can produce different levels of output. Higher levels of production are shown by isoquants that are further from the origin (see the graph 1).

 

       Isocost line – a line that represents alternative combinations of factors of production that have the same costs. Or in other words, the combinations of inputs (K, L) that yield the producer the same level of output.

       The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.

       The combinations of inputs that produce a given level of output at the same cost can be expressed as:

       wL + rK = C

       Rearranging, K= (1/r)C - (w/r)L

       

       

         

       4.2. Cost minimization (Producer’s choice optimisation)

       The least cost combination of inputs for a given output occurs where the isocost curve is tangent to the isoquant curve for that output.

       The slopes of the two curves are equal at that point of tangency.

       The firm is operating efficiently when an additional output per dollar spent on labor equals the additional output per dollar spent on machines.So that marginal product per dollar spent should be equal for all inputs:

       

       We define marginal physical product as the additional output that can be produced by employing one more unit of that input while holding other inputs constant:

and

Choosing the Economically Efficient Point of Production can be shown in the graph: