## The Optimization Principle

In microeconomic modeling, the economic environment is divided up into two types of economic agents: consumers and producers . The underlying goals behind the actions of these agents is based on optimizing behavior -- the maximization of something subject to {s.t.} particular constraints.

For consumers (or households), the goal is to maximize utility subject to the constraint imposed by household income and market prices -- the Budget Constraint. In the case of producers (or business firms), the goal is to maximize profits (sales revenue minus the costs of production) subject to the constraint of existing technology and know-how as defined by the Production Function.

#### The problem facing the Consumer:

max U = f(X1,X2,X3,...XN,) -- the objective function
s.t.
Σ[i=1, ... n] PiXi   <  I -- the constraint

where:

U ... "Utility" -- the satisfaction gained from choosing a particular bundle of goods.
Xi ... quantity of the ith good consumed
Pi ... Price of the ith good.
I ... Consumer Income

In words: Consumers allocate their income 'I' in such a manner as to maximize their satisfaction from consuming those goods and services purchased at existing market prices.

#### The problem facing the Producer:

max π = PxX - [wL + rK +nM + aR] -- the objective function [Revenues - Costs].
s.t.
X = f(L,K,M,R) -- the constraint [the production function]

where:

π ... Profits
Px ... the market determined price of good 'X'.
X ... the quantity of good 'X' produced.
L,K,M, & R ... the factors of production: L = Labor, K = Capital, M = Land and Raw Materials, R = Entrepreneurship.
w,r,n, & a ... factor prices: w = Wages, r = rental cost of capital, n = rents and material prices, a = the normal rate of profit (i.e., the opportunity cost [next best use] of the entrepreneur's time).
f( . ) ... technology and knowhow used to convert the inputs into the desired output.

In words: Producers (business firms) exist to convert inputs into desired goods and services in an efficient manner. Given that output prices and factor prices are determined in competitive markets, efficiency means exploiting existing production technology to the greatest extent possible. Profits earned by the entrepreneur represent the reward for taking risks (facing an uncertain demand for the output) and achieving efficiency in production (relative to competing producers) -- profits that are least equal to what the entrepreneur could earn by working for someone else.

Concepts for Review:
• Budget Constraint
• Constraint
• Consumer, Households
• Economic Agents
• Objective Function
• Optimization