Functional Relationships - Assignment Example

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However, there are variable inputs that are used in the production such as labor and fuel. This curve shows the relationship between input and output. Production of goods y is possible…
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Production Function Independent variable x. dependent variable y The curve shows the quantity of goods y produced as input x .represented by equation y=f(x). However, there are variable inputs that are used in the production such as labor and fuel. This curve shows the relationship between input and output. Production of goods y is possible with two inputs, this result in partial production function. The function has one variable input and the rest are assumed to be fixed at a certain amount.
The output x is attached is attached to every value of y outputs amounts produced by these input. Points below the curve are also part of the quantity produced, this points represent inefficient production. Therefore production function interlink inputs and outputs as in the case provided.
Taking for example the industrial production of sugar at a sugar mill. For production of sugar several inputs are required for production process to be complete. Although there are many inputs from labor, fuel, sugarcane supply, water and machinery the main inputs are sugarcane supply.
Therefore, as graphically represented, for production of 20 tons of sugar, 10 trucks of sugarcane inputs are required for its production process.
Additionally, 80 tons of sugar requires a maximum of 20 trucks for its production to be successful.
The firm equilibrium output is at 140 tons where the firm uses 30 trucks of sugarcane to operate efficiently. Moreover, the firm produces maximum sugar by using 30 trucks of sugarcane.
An increase in the quantity of inputs as shown by the graph result in corresponding increase in the quantity of sugar produced.
In conclusion, although there are several inputs for production of sugar, the main input is sugarcane supply.
Introduction of a new Variable
Assuming there are two inputs involved in production the function becomes
To produce output y, input x1 and x2 are required for it to be produced. Therefore, such input set has the following effects on production of y. x is the sum input x1 and x2 referred to as the isoquant.
The input set are represented graphically as shown where there are two inputs x1 and x2. The combination can give y1 shown in the graph. Larger quantity of x1 and x2 produces more quantity of y1.
Consider a situation where there are two main inputs x1 and x2 for production of sugar. Let x1 be sugarcane supply and x2 be labor. All these inputs work together for production of sugar. For Y quantity of sugar to be produced the firm need to use x1 quantity of sugarcane and x2 labor in the firm.
Therefore, therefore labor and sugarcane become two independent variables for production of maximum quantity of sugar.
Point E in the graph represent the equilibrium amount of sugar produced by use of two variables labor and sugar.
As more inputs of labor and sugarcane are introduced, the quantity of sugar produced increases gradually until the firm reaches its equilibrium point E where it produces Y quantity of sugar.
Therefore, production process requires different inputs put together to produce a given output required. Inputs such as labor, capital and raw materials are equally important in the production process.
In conclusion, addition of extra inputs in production clearly has great impact in production process. Production functions are determined by inputs that are used. Such inputs for example labor, capital and raw materials are used in the production process to determine the amount of outputs in production.
Hillegers, L. T. M. E. The Estimation of Parameters in Functional Relationship Models. Maastricht: [L.T.M.E. Hillegers], 1986. Print.
Porter, Michael E., and Scott Stern. Measuring the "ideas" Production Function: Evidence from International Patent Output. Cambridge, MA.: National Bureau of Economic Research, 2000. Print. Read More
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