Chapter 9: Production.
Goal:
* Production Function – The relationship
between input and output.
+ Isoquant.
+ Average Product, Marginal Product.
 Short run Production Function and the idea
of Diminishing Return.
 Long run Production Function and the idea
of Return to Scale.
Production Function in General.
Production function describes the
relationship between inputs and output.
 The production function

 Frequently encountered inputs: Capital (K) and
Labour (L)production function = Y(K,L).
◦ Idea of fixed and variable inputs.
 Example: Land is fixed input and Farmers are
variable input. In the above case, capital is fixed and
labour is variable.
Production Function in General
Important production functions
 1. The Leontief technology (fixed-proportions
technology)
◦ Y(x1,x2) = min(ax1,bx2)
◦ Example: Y(K,L) = min(1/6L,K)

2. The Cobb-Douglas technology
◦ Found to be realistic
◦ Example Cobb-Douglas p.f.:

3. Perfectly substitutable inputs p.f.: Y(K,L)=aK+bL
◦ Example: Y(K,L)=2.5K+L
Production Function in General.
Total Product: The amount of output produced
at given the level of inputs.
 Marginal Product: The change in the total
product that occurs in response to a unit
change in the variable input (all other inputs
held fixed).
 Average Product (of a variable input): is defined
as the total product divided by the quantity of
that input.

◦ Geometrically, it is the slope of the line joining the
origin to the corresponding point on the total
product curve.
Short run Production Function.



Short run: the longest period of time during which at
least one of the inputs used in a production process
cannot be varied.
Assuming K is fixed at K0, the short run production
function is then Y(K,L)= K0L β
Law of diminishing return: if other inputs are fixed, the
increase in output from an increase in the variable input
must eventually decline. In other word, the marginal
product will increase then decrease as more variable
input is added. This is a short run phenomenon.
Short run Production Function.
Short run Production Function.
Short run Production Function

Exercise:
◦ A firm/s short-run production function is
given by:
 Q

5 2
L for 0
4
1 2
Q 3L
L
4
L
2
for 2
L
7
 Sketch the production function.
 Find the maximum attainable production. How much
labour is used at that level?
 Identify the ranges of L utilization over which the MPL is
increasing and decreasing.
 Identify the range over which the MPL is negative.
Short run Production Function.

Key things to remember:
◦ When marginal product curve lies above the
average product curve, the average product
curve must be rising and vice versa.
◦ If there are more than one production
processes, allocate the resource so that the
marginal products are the same across
different production processes.
◦ Always allocate resource to the activity that
yields higher marginal product.
Long run Production Function.
Long run: The shortest period of time required
to alter the amounts of all inputs used in a
production process.
 Y(K,L)= KαLβ . Now both K and L are variable
inputs.
 Graphical expression of the production function
– the isoquant

◦ Isoquant is the set of all input combinations that yield
a given level of output. Similar to the indifference
curve.
Long run Production Function.

Marginal Rate of Technical Substitution.

Returns to scale:
◦ What happens if we doubled all inputs?
 Output doubles too  constant returns to scale.
 Y(cK,cL) = cY(K,L)
 Output less than doubles  decreasing returns to scale.
 Y(cK,cL) < cY(K,L)
 Output more than doubles  increasing returns to scale.
 Y(cK,cL) > cY(K,L)
Production Function

Exercise:
◦ Consider the following production function
Q
K 0.7 L0.2
Q 2K L
 Determine whether they exhibit
diminishing/constant or increasing marginal return
of labour.
 Determine whether they exhibit
decreasing/constant/increasing return to scale.