## Saturday, August 27, 2011

### Production

Is the process of using the services of labor and equipment together with national resources and materials to make goods / services available.

Technology - is the knowledge of how to produce goods and services.

Production function - a relationship between inputs and the maximum attainable output under a given technology.

Q = f (L, K, M)

Where Q is the maximum amount under current technology that could be produced with any given combination of labor services L, capital services K and raw material M.
Properties of the production function.
• There is a limit to extra production that can be achieved when more of one input is used while other inputs held constant. This implies that, for example, in a chair factory with a given amount of space & machines there is a limit to extra production that can be obtained by hiring more workers.
• There is some complementarity among inputs, but it is possible to substitute the use of an input for the use of another input, without reducing production. For example, a given quantity and quality of furniture can be manufactured by using a highly mechanized process or by using less capital and more labor.
• It is easier to vary the use of inputs over longer periods than over shorter periods.
► The short run is a period of production during which some inputs can not be varied. In the shot run for example manufacturing firms are confined to a given factory and track the time and resources to expand their facilities.

► The long run is a period of production so long that a producers have adequate time to vary all their inputs used to produce a certain commodity.

Total product of a variable input - is the amount of output produced where a given amount of that input is used along with the fixed inputs.

The average product of variable input - the total product of the variable input divided by the amount of that input used.
APl = TPl / L
Marginal product of variable input - is the change of the TP of that input corresponding to one unit change in its use.
MPl = ∆ TPl / ∆ L
Example:
Chair factory.
Total average and marginal product of labor, when K = 300 machine hours monthly.

Total average and marginal product of a variable input. The stages of production.

The total product curve.
It shows how output varies as more of the variable input is used together with fixed inputs. Along a TPC increasing the proportion of the variable input to the fixed inputs can increase production. [from the table see fifth column 0.3 to 2 with K = 300]. The TPC indicates that a maximum amount of output can be produced when amounts of inputs are fixed. This maximum amount occurs at point C where L** hours per month are used together with the K machines hours.

Average product curve.
The APC and MPC can be derived from the TPC. The slope of the APC is given by Q1 /L1 at the output Q. The maximum APl is attained where line OB is tangent to the TPC. This occurs at point B at which output Q* and L*. Labor hours are used together with fixed input. At this point the average product of labor is Q* / L*, which measures the slope of line OB. At point A, the average product of labor APl is therefore larger than it is at point B. Similarly the APl at point C which correspond to L** is lower than it is at point B because the slope of line OC is less than the slope of line OB

Marginal product curve.
The slope of the TPC at any point measures the change in output for very small changes in labor hours DQl /D L. This slope is the marginal product of labor. The slope of the TPC and therefore the Marginal product of labor increase until point A has been reached. Beyond this point it starts to decrease.

The short run stages of production.

Stage 1.
This stage begins at the start of the production where L = 0, and runs to the point corresponding to L =L* where average product of labor is at maximum. In this stage the proportion of labor to capital (variable input to fixed input is too low relative the purpose for which the production plant was designed. Too much capital relative to labor.
Stage 2.
It begins at the point where the average product of labor is at maximum. In this stage there is neither a redundancy of capital or labor.
Stage 3.
In this stage the marginal product of labor becomes negative. In this stage there is too much labor relative to capital.

The law of diminishing returns.
According to this law the MP of the variable input will decline as the proportion of the variable input to fixed input (labor to capital) increases.
The law implies that there is a limit the amount of output that can be produced in a productive facility of a given size.
In the figure it assumed that the production function Q = f (K, L, M) is such that after L** units of labor are employed per month, the MPl becomes negative

Costs and output in the short run.
• Total cost: (TC) - the sum of the cost of all inputs used to produce an item (commodity)
• Variable cost : (VC) - cost of all inputs that changes with output. Includes the expenditure for wages, salaries, and raw materials. These costs increase as output increases.
• Fixed cost : (FC) - is the cost of inputs that are independent of output. E.g. can include expenditure for plant maintenance, insurance, rent etc… managers often refer to their fixed costs as overhead costs. Thus , TC = VC + FC
• Average cost:- the total cost per unit of output Ю AC = TC / Q
• Average variable cost: -(AVC) is the variable cost per unit of output. AVC = VC / Q
• Average fixed cost: (AFC) is the fixed cost per unit of output AFC = FC / Q
AC = AVC + AFC
• Marginal cost: (MC) - is the change in TC that results from the change in output. The extra cost incurred to produce another unit of output.

MC = ∆TC / ∆ Q.

 Output TFC TVC TC AFC AVC ATC MC 0 30 0 30 - - - - 1 30 30 60 30 30 60 30 2 30 41 71 15 20.5 35.5 11 3 30 49 79 10 16.3 26.3 8 4 30 58 88 7.5 14.5 22 9 5 30 70 100 6 14 20 12

 Labor hours L Total product of labor TPl Average product of labor APl =TPl / L Marginal product MPl = DTPl / D L Proportion of labor to capital L / K 100 35 0.35 35 0.33 200 150 0.75 1.15 0.66 300 210 0.70 0.60 1 400 250 0.63 0.40 1.33 500 270 0.54 0.20 1.667 600 288 0.48 0.18 2
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