Short RUn Prouder Theory and Profit Maximization
Lecture Notes on Short-Run Producer Theory and Profit Maximization
Lalith Munasinghe
Production Functions
We begin with a few definitions. Firm: An organization that turns inputs into outputs.
Production Function (PF): The mathematical relationship between inputs and outputs. The PF is a technical relationship that specifies how much output can be produced from any possible combination of inputs.
Example: an automobile is an output made from a complex combination of a variety of inputs – labor, machines, steel, rubber, managerial labor, engineers, etc.
Our analysis is going to be based on a very simple technology: two inputs (denoted as K and L for capital and labor, respectively) and one output (denoted as Q). We represent this technology via a simple production function:
Q = f(K,L); so output is only a function of Capital (K) and Labor (L)
This relationship shows the maximum amount of output Q that can be produced from alternative combinations of K and L.
Short-Run Production
We begin our analysis of production functions with an even simpler problem by assuming that K is fixed. So the only thing that we can change to affect output is L. This simplification leads to the Short-Run analysis of production.
We start with three concepts of output related to labor input.
1. Total Product of Labor (TPL). The relationship between Q and L, holding K constant. Clearly it will be an increasing relationship. The more L you hire the more Q you will be able to produce.
2. Marginal Physical Product of Labor (MPL). The additional output produced by hiring one more unit of L, holding other inputs constant.
3. Average Physical Product of Labor (APL). Total output divided by total L employed, holding K constant. It is the ratio of output to labor – output per unit of labor. How much each unit of labor produces on average.
Now consider how these three concepts are linked to each other, and their relationship to the amount of labor (L) hired.
Lalith Munasinghe
Production Functions
We begin with a few definitions. Firm: An organization that turns inputs into outputs.
Production Function (PF): The mathematical relationship between inputs and outputs. The PF is a technical relationship that specifies how much output can be produced from any possible combination of inputs.
Example: an automobile is an output made from a complex combination of a variety of inputs – labor, machines, steel, rubber, managerial labor, engineers, etc.
Our analysis is going to be based on a very simple technology: two inputs (denoted as K and L for capital and labor, respectively) and one output (denoted as Q). We represent this technology via a simple production function:
Q = f(K,L); so output is only a function of Capital (K) and Labor (L)
This relationship shows the maximum amount of output Q that can be produced from alternative combinations of K and L.
Short-Run Production
We begin our analysis of production functions with an even simpler problem by assuming that K is fixed. So the only thing that we can change to affect output is L. This simplification leads to the Short-Run analysis of production.
We start with three concepts of output related to labor input.
1. Total Product of Labor (TPL). The relationship between Q and L, holding K constant. Clearly it will be an increasing relationship. The more L you hire the more Q you will be able to produce.
2. Marginal Physical Product of Labor (MPL). The additional output produced by hiring one more unit of L, holding other inputs constant.
3. Average Physical Product of Labor (APL). Total output divided by total L employed, holding K constant. It is the ratio of output to labor – output per unit of labor. How much each unit of labor produces on average.
Now consider how these three concepts are linked to each other, and their relationship to the amount of labor (L) hired.