3. Basic Concepts of Production Function
In econmics, a production function gives the technological relation between
quantities of physical inputs and quantities of output of goods. The
production function is one of the key concepts of mainstream classical
theories, used to define marginal product and to distinguish allocative
efficiency.
Production Function
In macroeconomics, aggregate production functions are estimated
to create a framework in which to distinguish how much of
economic growth to attribute to changes in factor allocation (e.g. the
accumulation of physical capital) and how much to attribute to
advancing technology.
In Macroeconomics
4. Basic Concepts of Production Function
Inputs: Labor, Capital, Raw Materials
Outputs: Goods, Services
Inputs and Outputs:
Total product (total output). In manufacturing industries such as motor vehicles, it is
straightforward to measure how much output is being produced. In service or knowledge
industries, where output is less “tangible" it is harder to measure productivity.
Average product measures output per-worker-employed or output-per-unit of capital.
Marginal product is the change in output from increasing the number of workers used by
one person, or by adding one more machine to the production process in the short run.
Three measures of production
Mathematical Representation:
General form:
Q=f(L,K,R) WhereQ = Output, L = Labor,K = Capital,R=RawMaterials
5. Basic Concepts of Production Function
Inputs: Labor, Capital, Raw Materials
Outputs: Goods, Services
Inputs and Outputs:
Total product (total output). In manufacturing industries such as motor vehicles, it is
straightforward to measure how much output is being produced. In service or knowledge
industries, where output is less “tangible" it is harder to measure productivity.
Average product measures output per-worker-employed or output-per-unit of capital.
Marginal product is the change in output from increasing the number of workers used by
one person, or by adding one more machine to the production process in the short run.
Three measures of production
Mathematical Representation:
General form:
Q=f(L,K,R) WhereQ = Output, L = Labor,K = Capital,R=RawMaterials
6. Short-RUN Production Function
Origin to point A : MP ↑ ， MP ＞ AP
The firm is experiencing positive and increasing marginal,
output increases at a increasing rate
Point A to point C ： MP ↓ ， MP ＞ AP→MP =AP → MP ＜
AP
The firm is experiencing positive but decreasing marginal
returns to the variable input. As additional units of the input
are employed, output increases but at a decreasing rate.
Point B: MP=AP
This point is the point beyond which there are diminishing
average returns, as shown by the declining slope of the average
physical product curve (AP) beyond point Y.
Beyond point B, mathematical necessity requires that the
marginal curve must be below the average curve .
7. Short-RUN Production Function
Stage 1 (from the origin to point B) ： the variable input is being used with
increasing output per unit, the latter reaching a maximum at point B (since
the average physical product is at its maximum at that point). Because the
output per unit of the variable input is improving throughout stage 1, a
price-taking firm will always operate beyond this stage.
Stage 2, output increases at a decreasing rate, and the average and marginal
physical product both decline. However, the average product of fixed inputs
(not shown) is still rising, because output is rising while fixed input usage is
constant. In this stage, the employment of additional variable inputs
increases the output per unit of fixed input but decreases the output per
unit of the variable input. The optimum input/output combination for the
price-taking firm will be in stage 2, although a firm facing a downward-
sloped demand curve might find it most profitable to operate in Stage 2.
In Stage 3, too much variable input is being used relative to the available
fixed inputs: variable inputs are over-utilized in the sense that their presence
on the margin obstructs the production process rather than enhancing it.
The output per unit of both the fixed and the variable input declines
throughout this stage. At the boundary between stage 2 and stage 3, the
highest possible output is being obtained from the fixed input.
8. A short-run production function refers to that period of time,
in which the installation of new plant and machinery to
increase the production level is not possible.
On the other hand, the Long-run production function is one
in which the firm has got sufficient time to install new
machinery or capital equipment, instead of increasing the
labour units.
Defination
Short-RUN
&
Long-RUN
Production Function
9. In the long run the firm can change its scale of operations by adjusting the level of inputs
that are fixed in the short run, thereby shifting the production function upward as plotted
against the variable input. If fixed inputs are lumpy, adjustments to the scale of
operations may be more significant than what is required to merely balance production
capacity with demand. For example, you may only need to increase production by million
units per year to keep up with demand, but the production equipment upgrades that are
available may involve increasing productive capacity by 2 million units per year.
Long-RUN
Production Function
10. Cost Function
In economics, a cost function is a mathematical relationship
that describes how production costs change with varying levels
of output. It encapsulates the total cost incurred by a firm in
producing a given quantity of a good or service.
Fixed Costs (FC): These are costs that do not vary with the level of output.
Examples include rent, salaries of permanent staff, and depreciation of
machinery.
Variable Costs (VC): These costs change directly with the level of output.
Examples include raw materials, labor directly involved in production, and
utility costs related to production.
Total Cost (TC): This is the sum of fixed and variable costs at any
given level of output. TC=FC+VC
11. Cost Function
Average Cost (AC): This is the total cost per unit of output. It can be broken
down into average fixed cost (AFC) and average variable cost (AVC).
AC=TC
/Q =AFC+AVC
where Q is the quantity of output produced.
Marginal Cost (MC): This is the additional cost incurred by producing one
more unit of output. It is a crucial concept for determining the optimal level
of production.
A short-run marginal cost (SRMC) curve is constructed to capture the relation
between marginal cost and the level of output, holding other variables, like
technology and resource prices, constant. The marginal cost curve is usually U-
shaped. Marginal cost is relatively high at small quantities of output; then as
production increases, marginal cost declines, reaches a minimum value, then
rises.
The long-run marginal cost (LRMC) curve shows for each unit of output the added
total cost incurred in the long run, that is, the conceptual period when all factors of
production are variable. Stated otherwise, LRMC is the minimum increase in total
cost associated with an increase of one unit of output when all inputs are variable.
12. SAC represents the costs of a single plant, whereas LAC represents the costs of different plants.
Like SAC, LAC is also U-shaped but it is relatively flatter. The U-shape of LAC is less pronounced as compared to
SAC. It indicates that in the long run, increase or decrease in costs is relatively less. It is so because LAC represents
the minimum average cost of different quantities of output so there exists less possibilities of fluctuations.
LAC cannot be more than SAC. It is so because LAC is tangent to SAC
Relationship between LAC and SAC:
13. In economics, the revenue function describes how a firm's total revenue (TR) changes with the quantity of goods or
services sold. Total revenue is calculated as the product of the price per unit (P) and the quantity sold (Q).
Understanding the revenue function is crucial for firms to make informed decisions about pricing, production, and
maximizing profits.
Formula for Total Revenue
The basic formula for total revenue is:TR=P×Q
where:
TR is the total revenue,
P is the price per unit,
Q is the quantity of units sold.
In a perfectly competitive market, firms are price takers. The market determines the price, and firms can sell any
quantity at this price.Marginal revenue (MR) is constant and equal to the market price:
MR=P
Revenue Function
14. Average revenue is the revenue per unit of output, which is equal to the price in both perfect competition and
monopoly:
AR= TR/Q =P
Revenue Maximization:
In perfect competition, revenue maximization coincides with profit maximization when MR=MC.
Revenue Function
15. In Figure, the relationship between AFC average fixed cost, AVC
average variable cost, SAC short-run average cost, MC margin
cost.
AFC slopes downward. It indicates that as production increases,
AFC goes on falling. In the beginning, it slopes steeply but later
on rate of fall slows down.
AVC is the average variable cost. It falls up to point E and then
rises upward.
SAC is the short run average cost curve having U-shape. The
minimum point E of AVC occurs earlier than the minimum point E’
of SAC. MC passes from the minimum points of both AVC and
SAC through the points E and E’ respectively.
