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The production function for a firm is the relationship between the quantities of inputs per time period and the maximum output that can be produced. It can be calculated for one or more than one variable factors of production. The one variable factor of production function corresponds to the short-run during which at least one factor of production is fixed .
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Describe the production function with one variable input and explain the relationship between TPMP and AP curves and the three stages of production?
there are three stages of production mp>ap
What is short run production function?
if at-least one factor of production is constant, production function is infact short-run production function
What are the managerial uses of production functions?
In microeconomics, a production function asserts that the maximum output of a technologically-determined production process is a mathematical production of input factors of production. Considering the set of all technically feasible combinations of output and inputs, only the combinations encompassing a maximum output for a specified set of inputs would constitute the production function. Alternatively, a production function can be defined as the specification of the minimum input requirements needed to produce designated quantities of output, given available technology. It is usually presumed that unique production functions can be constructed for every production technology. By assuming that the maximum output technologically possible from a given set of inputs is achieved, economists using a production function in analysis are abstracting away from the engineering and managerial problems inherently associated with a particular production process. The engineering and managerial problems of technical efficiency are assumed to be solved, so that analysis can focus on the problems of allocative efficiency. The firm is assumed to be making allocative choices concerning how much of each input factor to use, given the price of the factor and the technological determinants represented by the production function. A decision frame, in which one or more inputs are held constant, may be used; for example, capital may be assumed to be fixed or constant in the short run, and only labour variable, while in the long run, both capital and labour factors are variable, but the production function itself remains fixed, while in the very long run, the firm may face even a choice of technologies, represented by various, possible production functions. The relationship of output to inputs is non-monetary, that is, a production function relates physical inputs to physical outputs, and prices and costs are not considered. But, the production function is not a full model of the production process: it deliberately abstracts away from essential and inherent aspects of physical production processes, including error, entropy or waste. Moreover, production functions do not ordinarily model the business processes, either, ignoring the role of management, of sunk cost investments and the relation of fixed overhead to variable costs. (For a primer on the fundamental elements of microeconomic production theory, see production theory basics). The primary purpose of the production function is to address allocative efficiency in the use of factor inputs in production and the resulting distribution of income to those factors. Under certain assumptions, the production function can be used to derive a marginal product for each factor, which implies an ideal division of the income generated from output into an income due to each input factor of production.
Explain with diagram the law of variable proportion?
Sometimes referred to as the law of diminishing returns, the law of variable proportions is concerned with the effect of changes in the proportion of the factors of production used to produce output. As the proportion of one input increases relative to all other inputs, at some point there will be decreasing marginal returns from that input. Adding more units of an input, holding all other inputs constant, will at some point cause the resulting increases in production to decrease, or equivalently, the marginal product of that input will decline. Among the inputs held constant is the level of technology used to produce that output. This is an empirical law and is therefore a generalization about the nature of the production process and cannot be proven theoretically (see Friedman, 1976; Stigler, 1966). Applied to management, Friedman argues that the law of variable proportions requires firms to produce by using inputs in such proportions that there are diminishing average returns to each input in production.
What is extra output generated by one more unit of variable input?
Marginal Product
Describe the production function with one variable input and explain the relationship between TPMP and AP curves and the three stages of production?
there are three stages of production mp>ap
A function is a rule that assigns each value of the variable to exactly one value of the dependent variable?
I found two answers for this question. A function is a rule that assigns to each value of one variable (called the independent variable) exactly one value of another variable (called the dependent variable.) A function is a rule that assigns to each input value a unique output value.
How does a function differ from an equation?
A function is a rule to calculate a variable, based on one or more other variables. It may be written as an equation, but unlike a generic equation, in a function, for every value of the input variables, it may ONLY have ONE result.
Can a function have more than one output per one input?
No. A function has only one output per input.
In a function can an input have more than one outputs?
No. If an input in a function had more than one output, that would be a mapping, but not a function.
How do we know that the input have one output or more in a function in math?
By definition. If one input has more than one outputs then it is not a function.
When can we say that a function is a relation?
When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").
When can we say that a relation is a function?
When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").
How many zeros can you have in an algebraic function?
For an algebraic function in one variable, as many as the highest power of the variable.
How do you know whether a relation is a function?
Use the definition of a function. If, for any value of one variable, there is only a single possible value of the second variable, then the second variable is a function of the first variable. The second variable is often called the "dependent variable". If you can solve an equation explicitly for the dependent variable, then it is a function. If you can NOT solve it for a variable, it may or may not be a function - it turns out that some equations are hard or impossible to solve explicitly for one of the variables.
What is short run production function?
if at-least one factor of production is constant, production function is infact short-run production function
A function takes in values of variable called inputs and gives back values of the variable called outputs?
No. A function takes in values of no, one, or more input variables, and returns no or one result. It cannot return more than one result. Do not confuse this with returning multiple results using call by reference parameters - this is not the same thing.
