Inputs

Examples of Inputs in the following topics:

• Aggregate Production

  • Stage 1: the variable input is being used with increasing output per unit.
  • The average product of fixed inputs are still rising.
  • The optimum input/output combination will be reached.
  • Stage 3: variable input is too high relative to the available fixed inputs.
  • The output of both fixed and variable input declines.

• Sensitivity Analysis

  • Sensitivity analysis determines how much a change in an input will affect the output.
  • It also helps to determine the optimal levels of each input.
  • However, not all of the inputs may be independent so changing inputs one at a time does not account for interaction between the inputs.
  • In this case, the output (y-axis) decreases exponentially with an increase in the input (x-axis).
  • This is mapped out for each input.

• Production

  • "Short-run": A period in which technology is constant, at least one input is fixed and at least one input is variable.
  • The AP is a ratio of TP or Q or output to a variable input and a set of fixed input(s).
  • In the short-run, as a variable input is added to a fixed input (plant size) the TP may increase at an increasing rate.
  • Initially, there is "too much" of the fixed input and not enough of the variable input.
  • There is "too much variable input" for the fixed input.

• Total Factor Productivity

  • Total factor productivity, which captures how efficiently inputs are utilized, is a key indicator of competitiveness.
  • Instead, it is a residual which accounts for effects on total output not caused by inputs.
  • In the equation above, Y represents total output, K represents capital input, L represents labor input, and alpha and beta are the two inputs' respective shares of output.
  • However, due to to the law of diminishing returns, the increased use of inputs will fail to yield increased output in the long run.
  • The quantity of inputs used thus does not completely determine the amount of output produced.

• Costs and Production in the Short-Run

  • If the short-run production function (Q =f(L) given fixed input and technology) and the prices of the inputs are known, all the short-run costs can be calculated.
  • Often the producer will know the costs at a few levels of output and must estimate or calculate the production function in order to make decisions about how many units of the variable input to use or altering the size of the plant (fixed input).
  • Fixed Cost (FC) is the quantity of the fixed input times the price of the fixed input.
  • Variable Cost (VC) is the quantity of the variable input times the price of the variable input.

• Market for Inputs

  • The market for an input includes all potential buyers and sellers of an input.
  • The demand reflects the decisions of the buyers of the inputs and is based on the MRP for the factor.
  • The supply function represents the decisions of the factor owners to supply the input at various prices.

• Introduction to Production and Cost

  • Decisions about production require individual agents to make decisions about the allocation and use of physical inputs.
  • Objectives of agents, technology, availability and quality of inputs determine the nature of these decisions.
  • Since the objectives are often pecuniary, it is often necessary to relate the decisions about the physical units of inputs and outputs to the costs of production.
  • If the prices of the inputs and the production relationships are known (or understood), it is possible to calculate or estimate all the cost relationships for each level of output.
  • In practice however, the decision maker will probably have partial information about some of the costs and will need to estimate production relationships in order to make decisions about the relative amounts of the different inputs to be used.

• Measuring Productivity

  • Productivity is represented by production functions, and is the amount of output that can be generated from a set of inputs.
  • Increased productivity means more output is produced from the same amount of inputs.
  • This can range from highly tangible inputs (working hours, products assembled) to highly intangible inputs (entrepreneurship, experience, technology skills, etc.).
  • In this circumstance 'Q' is the quantity of output while each 'x' is a factor input.
  • This is an illustration of a two-input Cobb-Douglas Production Function, where the ability to benchmark an output in comparison to two separate quantities of inputs is feasible.

• Functions and Their Notation

  • A function maps a set of inputs onto a set of permissible outputs.
  • Each input corresponds with one and only one output
  • In the case of a function with just one input variable, the input and output of the function can be expressed as an ordered pair.
  • That is, the function divides the input by two.
  • A function $f$ takes an input $x$ and returns an output $f(x)$.

• Defining the Production Function

  • The production function relates the maximum amount of output that can be obtained from a given number of inputs.
  • In economics, a production function relates physical output of a production process to physical inputs or factors of production.
  • It is a mathematical function that relates the maximum amount of output that can be obtained from a given number of inputs - generally capital and labor.
  • This describes a firm that requires the least total number of inputs when the combination of inputs is relatively equal.
  • Finally, the Leontief production function applies to situations in which inputs must be used in fixed proportions; starting from those proportions, if usage of one input is increased without another being increased, output will not change.