# What is a graphical example of a long-run production curve?

Jul 30, 2015

In the long run, the firm has no fix cost, so both capital and labor will vary so that the production can increase. The curve is called an isoquant.

#### Explanation:

A long run production function has two variable factors: labor and capital. The company will look for all possible combinations of both inputs to reach the production it wants. The isoquant is the curve that will measure all these combinations and it is displayed in the graph below.

There can be infinite isoquants in the graph, because, since both inputs can vary, the company can produce as much as it wishes, as long as it can afford the production costs.

An example is a Cobb-Douglas function:
$q = a \cdot {L}^{\alpha} \cdot {K}^{\beta}$, where q is the quantity of output from L units of labor and K units of capital and where $a$, $\alpha$ , and $\beta$ are positive constants.
graph{50=4x^.5*y^.5 [-6.23, 66.84, -8.05, 28.47]}
This is the graph for the function $50 = 4 \sqrt{L} \cdot \sqrt{K}$

Source: BESANKO, David A; BRAEUTIGAM, Ronald R. Microeconomics . 4th ed. Wiley, 2011. Chapter 6.