Isoquants

An isoquant is a curve or line that has various combinations of inputs that yield the same amount of output.

Production functionHere we will assume output is made with the inputs capital and labor. K = amount of capital used and L = amount of labor. The production function is written in general as Q = F(K, L) – sometimes I put a y instead of Q, where Q = output,and F and the parentheses are general symbols that mean output is a function of capital and labor.The output, Q, from the production function is the maximum output that can be obtained form the inputs.

On the next screen we will see some isoquants. Note: on a given curve L and K change while Q is fixed.

Time Frame

In production, we have said that firms have the ability to use both capital and labor.

When you consider the fact that capital is basically the production facility – the building, equipment, machines and the like – you can get the feeling that it is probably less easy to change the capital than it is to change the amount of labor used.

When you look at how long it takes to change the amount of capital in production, during that time when capital can not be changed in amount the time period of production is said to be the SHORT RUN. When all inputs can be changed we are in the LONG RUN.

Long run

Labor

Capital On a curve we have different combinations of L and K that give the same amount of output. Curves farther out in the northeast direction have more output. Later we will say more about what the firm uses as a guide to choice of position in the graph. The position chosen will have implications for the amount of labor demanded.

Short RunCapital

Labor

K*

In the short run the firm would have a given amount of capital, say K* here. Production would occur along the dotted line, or maybe below it.

Marginal Rate of SubstitutionCapital

Labor

Change in K Change in L

On the next slide I will refer to a change with the use of a triangle.

slope =

MRS

The slope of the curve at a point is

K/ L

Now, if the marginal product of an input is defined as the change in output divided by the change in the input, the slope can be manipulated to be:

K Q and since K = 1

L Q Q MPK

So the slope is MPL/MPK and is called the MRS (in absolute value) and it is a measure of the rate at which inputs can be substituted and output remains the same.

A few slides back I showed an isoquant. I also put a tangent line at a point on the curve. The slope of a curved line is really the slope of a tangent line.

You will notice that as you along the curved line from right to left that the slope of a tangent line gets smaller (in absolute value).