Demand Estimation

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: Capital

The short-run production function shows the maximum quantity of good or service that can be produced by a set of inputs, assuming the amount of at least one of the inputs used remains unchanged.

The long-run production function shows the maximum quantity of good or service that can be produced by a set of inputs, assuming the firm is free to vary the amount of all the inputs being used.

Short-Run Analysis of Total, Average, and Marginal Product

Alternative terms in reference to inputs

Alternative terms in reference to outputs

Marginal product (MP): change in output (or Total Product) resulting from a unit change in a variable input.

Average Product (AP): Total Product per unit of input used.

If MP > AP then AP is rising If MP < AP then AP is falling if MP=AP when AP is maximized.

Law of Diminishing Returns: As additional units of a variable input are combined with a fixed input, at some point the additional output (i.e., marginal product) starts to diminish.

* Nothing says when diminishing returns will start to take effect, only that it will happen at some point.

* All inputs added to the production process are exactly the same in individual productivity

The Three Stages of Production in the Short Run

Stage I: From zero units of the variable...