ECONOMICS AND MANAGERS
PRODUCTION AND COST IN THE SHORT RUN
EBO BOTCHWAY (Ph.D.)
University of Professional Studies
botchwayebo@yahoo.co.uk
October 15, 2019
EBO BOTCHWAY (Ph.D.) (UPSA)
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Overview
1
Describe the relationship between inputs and outputs
2
Derive the total product, marginal product and average products and
show the relationship between them
3
Determine the optimal input usage by a firm in the short run.
4
Derive the short run cost curves and show the relationship between
them and the product curves.
5
Show how a firm maximize output in the short run.
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Outline
1
Production Function
Short-Run Production Analysis
Relationship among TP, AP and MP
Law of Dimishing Marginal Returns
2
Cost Function
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Introduction
A production function describes the relationship between a flow of
inputs and the resulting flow of outputs in a production process
during a given period of time.
Q = f (K , L, M, ....)
where
Q = Quantity of Output
L = Quantity of Labour input
K = Quantity of Capital input
M = Quantity od Materials input
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Forms of Production Function
It is necessary to obtain estimates of production function for practical
decision making purposes.
Below are the examples of forms of production functions
Linear production function: Q = β0 + β1 L + β2 K
Quadratic production function: Q = β0 + β1 L + β2 L2 + β3 K
Cubic production function: Q = β0 + β1 L + β2 L2 + β3 L3 + β4 K
Cobb−Douglas production function: Q = ALα K β
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Efficiency in Production
In the process of production, managers need to be concerned with the
efficiency with which they use inputs.
Efficiency is the act of achieving good result with little waste of
efforts:
A firm can be:
Technical efficiency
Allocative efficiency
Economic efficiency
The firm attempts either to minimize the cost of producing a
given level of output or maximize output attainable with a
given level of cost
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Definitions
Fixed and Variable Inputs
A fixed input is an input whose quantity a manager cannot change
during a given period of time.
e.g machinery and equipment
A variable input is an input whose quantity a manager can change
during a given period of time.
e.g. labour and raw materials
Short−Run vs. Long−Run
Two dimensions of time are used to describe production functions:
short run and long run.
These periods do not refer to specific calendar periods of time, such
as month or a year, they are defined in terms of the use of fixed and
variable inputs.
The short-run is a period of time during which at least one input is
fixed, while the long-run is a period of time during which all inputs
are variable.
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Short-Run Production Analysis
Three measures of productivity or the relationship between inputs and
output in the short run.
Total Product: The total quantity of output produced with given
quantities of fixed and variable inputs.
TP = Q = f (L, K )
where
TP or Q = total product or total quantity produced
L = quantity of labour input (variable input)
K = quantity of capital (fixed input)
Average Product (AP): The amount of output per unit of variable
input.
For example; Average product of labour is defined as the amount of
output per unit of labour. i.e.
APL =
Q
L
where APL = Average product of Labour
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Short-Run Production Analysis
Marginal Product (MP): The additional output produced with an
∆Q
additional unit of variable input.MPL = ∆TP
∆L = ∆L where MPL =
Marginal product of Labour
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Short-Run Production Analysis
Mathematically, 2 out of the three productivity measures can be
obtained by differentiating or dividing the total product functions.
Suppose the production function of a firm is given as:
Q = 5K + 10L + 4.5L2 − 0.33L3
the average and marginal products can be derived
APL =
Q
5K
=
+ 10 + 4.5L − 0.33L2
L
L
and
MPL =
EBO BOTCHWAY (Ph.D.) (UPSA)
∂Q
= 10 + 9L − 0.99L2
∂L
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Short-Run Production Analysis
Total Product Curve
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Short-Run Production Analysis
Average and Marginal Product Curves
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Relationship among TP, AP and MP
There are three stages of production. They are
1
2
3
4
increasing marginal returns, TP is increasing at an increasing rate.
(Stage I)
MP is falling but AP is rising, TP is increasing at a decreasing rate
(Stage II).
both MP and AP are falling, but AP > MP (Stage III)
Beyond stage III, there is negative marginal returns
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Short-Run Production Analysis
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Short-Run Production Analysis
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Law of Dimishing Marginal Returns
The phenomenon illustrated by that region of the marginal product
curve where the curve is positive, but decreasing, so that total
product is increasing at a decreasing rate.
As more and more of a variable input is added to a fixed input,
addition to total output increases reaches a maximum and begins to
decline
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Cost Function
We now analyze how a firms costs of production vary in the short run.
A mathematical or graphic expression that shows the relationship
between the cost of production and the level of output, all other
factors held constant.
Opportunity Cost is the economic measure of cost that reflects the
use of resources in one activity, such as a production process by one
firm, in terms of the opportunities forgone in undertaking the next
best alternative activity.
Explicit Cost is a cost that is reflected in a payment to another
individual, such as a wage paid to a worker, that is recorded in a
firm0 s bookkeeping or accounting system.
Implicit Cost is a cost that represents the value of using a resource
that is not explicitly paid out and is often difficult to measure because
it is typically not recorded in a firm0 s accounting system (same as
opportunity cost)
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Profit
The difference between the total revenue a firm receives from the sale
of its output and the total cost of producing that output.
π = TR − TC
where TR is Total Revenue for the sale of the product and TC is total
cost of production.
Accounting profit is the difference between total revenue and total
cost where cost includes only the explicit costs of production.
Economic profit is the difference between total revenue and total
cost where cost includes both the explicit and any implicit costs of
production.
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Short-Run Cost Function
A cost function for a short-run production process in which there is at
least one fixed input of production.
Fixed cost is the total cost of using the fixed input, which remains
constant regardless of the amount of output produced.
Variable cost is the total cost of using the variable input, which
increases as more output is produced.
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Definitions
EBO BOTCHWAY (Ph.D.) (UPSA)
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Short-Run Production Analysis
Suppose PK = 50 and PL = 100
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Short-Run Production Analysis
Cost Curves
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Short-Run Production Analysis
Average and Marginal Cost Curves
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Relationship Between Short Run Production (AP, MP) and
Cost(AC, MC)
Total Variable Cost (TVC) = PL xL
MC =
MC =
∆TVC
∆TC
=
∆Q
∆Q
PL x∆L
∆L
= PL
∆Q
∆Q
MC =
AVC =
PL
∆Q
∆L
PL
MPL
TVC
PL xL
=
Q
Q
AVC =
EBO BOTCHWAY (Ph.D.) (UPSA)
=
P
APL
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Relationship Between Short Run Production (AP, MP) and
Cost(AC, MC)
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Revenue Functions
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Profit Maximization
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Profit Maximization
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The Profit Maximization Rule
Profits are maximized where marginal cost (MC) equals marginal
revenue (MR).
It is possible that over the firm0 s full potential range of outputs there
are two points where MC = MR.
Producing at point X would not maximize profit because outputs up
to X are produced where MC > MR.
Technically, profits are maximized where MC = MR and the MC
curve is rising (not falling), as at q* output
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Example
Suppose a firms demand function is given as Q = 55 − 0.5P, where P is
price and Q is rate of output and the total cost function
TC = 20 + Q + 0.2Q 2 , where TC is total cost. Determine the,
Total revenue and profit functions for the firm.
Level of output that maximizes total profit
Maximum profit for this company
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Normal and Supernormal Profit
Normal profit is the minimum profit which must be earned to ensure
that a firm will continue to supply the existing good or service.
Supernormal profit is any profit earned above normal profit and is a
form of economic rent.
These are measured relative to ATC
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Summary: Optimal Labour Usage
In the short run, managers are confronted with determining how much
of a variable input such as labour to use in order to maximize profits.
A firm should employ labour or any other variable input as long as the
extra revenue generated from the sale of the output produced exceeds
the extra cost of hiring the unit of labour.
Therefore, a profit maximizing firm operating in a perfectly
competitive output and input markets will be using an optimal
amount of an input at the point at which the monetary value of the
inputs marginal product is equal to the additional cost of using that
input. In simple terms, the firm maximises it revenue at the point
where MR = MC.
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Question 1
A consultancy firm, focusing on capacity building in Research
Methodology has a demand function
Q = 10 − 0.1P
and cost per unit function as
Q −8+
400
Q
where Q = number of capacity building hours and P = fees charged per
hour.
1 Determine the number of capacity building hours which maximizes
the company0 s profit.
2 How much should the firm charge for the capacity building?
3 Find the total profit at the profit maximizing level of consultancy.
4 Using the own price elasticity of demand, Comment on the firm0 s
pricing policy options.
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Question 2
Suppose the short-run production function for a restaurant producing a
pack of food is given by:
Q = 3L − 0.3L2
Where Q is the number of packs of food produced and L is the amount of
labour used. If the cost of a unit of labour is $6.00 and the unit price of a
pack of food produced is $10.00, what is the amount of labour the
restaurant should employ in order to maximize profit. How much profit is
made?
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Practice Question 3
If the price of the product is $2 and cost per unit of labour is $10,
Complete the table below.
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Practice Question 4
You were recently hired to replace the manager of a roller manufacturing
company, despite the managers strong external sales record. The
manufacturing company is relatively simple, requiring only labour and a
machine that cuts and crimps rollers. As you begin reviewing the
companys production information, you learn that labour is paid GH8.00
per hour and the last worker hired produced 100 rollers per hour. The
company rents roller cutters and crimping machines for GH16.00 per hour
and the marginal product of capital is 100 rollers per hour. What do you
think the previous manager could have done to keep his job?
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