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The Theory and Estimation of Production

Production function: defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology.

The production function can be expressed as

Q=f(X1, X2, ..., Xk)

Q: the output

X1, X2, ..., Xk: inputs used in the production process

Assumptions

* Some given “state of the art” in the production technology.

* Whatever input or input combinations are included in a particular function, the output resulting from their utilization is at the maximum level.

The production function often considered of two inputs for simplicity

Q=f(X, Y)

Q: output X: Labor Y: ...view middle of the document...

Total Revenue Product (TRP): market value of the firm’s output, computed by multiplying the total product by the market price.

TRP = Q · P

Marginal Revenue Product (MRP): change in the firm’s TRP resulting from a unit change in the number of inputs used.

MRP = = MP · P

Total Labor Cost (TLC): total cost of using the variable input, labor, computed by multiplying the wage rate by the number of variable inputs employed.

TLC = w · X

Marginal Labor Cost (MLC): change in total labor cost resulting from a unit change in the number of variable inputs used. Because the wage rate is assumed to be constant regardless of the number of inputs used, MLC is the same as the wage rate (w)

the relationship between demand for output and demand for input

A profit-maximizing firm operating in perfectly competitive output and input markets will be using the optimal amount of an input at the point at which the monetary value of the input’s marginal product is equal to the additional cost of using that input.

MRP = MLC

Multiple variable inputs

Consider the relationship between the ratio of the marginal product of one input and its cost to the ratio of the marginal product of the other input(s) and their cost.

Other factors may outweigh this relationship

Political/Economic risk factors

The Long-Run Production Function

* In the long run, a firm has enough time to change the amount of all its inputs.

* Effectively, all inputs are variable.

* The long run production process is described by the concept of returns to scale.

If all inputs into the production process are doubled, three things can happen:

output can more than double=====increasing returns to scale (IRTS)

output can exactly double =====constant returns to scale (CRTS)

output can less than double =====decreasing returns to scale (DRTS)

the use of coefficient of output elasticity to measure returns to scale

If EQ > 1 then IRT If EQ = 1 then CRTS If EQ < 1 then DRTS

Returns to scale can also be described using the following equation

hQ = f(kX, kY)

If h > k then IRTS If h = k then CRTS If h < k then DRTS

Estimation of Production Functions:

Forms of Production Functions

Short run: existence of a fixed factor to which is added a variable factor

One variable, one fixed factor

Q = f(L)K

Increasing...

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