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)= K0Lβ

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: for

for

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.

25

4Q L 0 2L

213

4Q L L 2 7L

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

Determine whether they exhibit

diminishing/constant or increasing marginal return

of labour.

Determine whether they exhibit

decreasing/constant/increasing return to scale.

0.7 0.2Q K L

2Q K L