The classical general equilibrium model aims to describe the economy by aggregating the behavior of individuals and firms. Note that the classical general equilibrium

General equilibrium

General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general...

 model is unrelated to classical economics

Classical economics

Classical economics is widely regarded as the first modern school of economic thought. Its major developers include Adam Smith, Jean-Baptiste Say, David Ricardo, Thomas Malthus and John Stuart Mill....

, and was instead developed within neoclassical economics

Neoclassical economics

Neoclassical economics is a term variously used for approaches to economics focusing on the determination of prices, outputs, and income distributions in markets through supply and demand, often mediated through a hypothesized maximization of utility by income-constrained individuals and of profits...

 beginning in the late 19th century.

In the model, the individual

Individual

An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...

 is assumed to be the basic unit of analysis and these individuals, both workers and employers, will make choices that reflect their unique tastes, objectives, and preferences. It is assumed that individuals' wants typically exceed their ability to satisfy them (hence scarcity of goods and time). It is further assumed that individuals will eventually experience diminishing marginal utility. Finally, wages and prices are assumed to be elastic (they move up and down freely). The classical model assumes that traditional supply and demand

Supply and demand

Supply and demand is an economic model of price determination in a market. It concludes that in a competitive market, the unit price for a particular good will vary until it settles at a point where the quantity demanded by consumers will equal the quantity supplied by producers , resulting in an...

 analysis is the best approach to understanding the labor market. The functions that follow are aggregate functions that can be thought of as the summation of all the individual participants in the market.

Labor demand

The consumers of the labor market are firms. The demand for labor services is a derived demand, derived from the supply and demand for the firm's products in the goods market. It is assumed that a firm's objective is to maximize profit

Profit (economics)

In economics, the term profit has two related but distinct meanings. Normal profit represents the total opportunity costs of a venture to an entrepreneur or investor, whilst economic profit In economics, the term profit has two related but distinct meanings. Normal profit represents the total...

 given the demand for its products, and given the production technology that is available to it.

Some notation:
Let be price level of commodities
Let be nominal wage
Let be real wage (w/p)
Let be profit of firms
Let be labor demand
Let be the firms output of commodities that it will supply to the goods market.

Output function

Let us specify this output (commodity supply) function as:
It is an increasing concave function with respect to L^D because of the Diminishing Marginal Product

Production theory basics

Production refers to the economic process of converting of inputs into outputs. Production uses resources to create a good or service that is suitable for use, gift-giving in a gift economy, or exchange in a market economy. This can include manufacturing, storing, shipping, and packaging. Some...

 of Labor. Note that in this simplified model, labour is the only factor of production. If we were analysing the goods market, this simplification could cause problems, but because we are looking at the labor market, this simplification is worthwhile.

Firms' profit function

Generally a firm's profit is calculated as:
profit = revenue - cost

In nominal terms the profit function is:


In real terms this becomes:

Firms' optimal (profit maximizing) condition

In an attempt to achieve an optimal situation, firms can maximize profits with this Maximized profit function:


When functions are given, Labor Demand (L^D) can be derived from this equation.

Labour supply

The suppliers of the labor market are household

Household

The household is "the basic residential unit in which economic production, consumption, inheritance, child rearing, and shelter are organized and carried out"; [the household] "may or may not be synonymous with family"....

s. A household can be thought of as the summation of all the individuals within the household. Each household offers an amount of labour services to the market. The supply of labour can be thought of as the summation of the labour services offered by all the households. The amount of service that each household offers depends on the consumption requirements of the household, and the individuals relative preference for consumption verses free time.

Some notation:
Let U be total utility
Let Y^D be commodity demand (consumption)
Let L^S be labor supply (hours worked)
Let D(L^S) be disutility from working, an increasing convex function with respect to L^S.

Households' consumption constraint

Consumption constraint = profit income + wage income

Households' utility function

total utility = utility from consumption - disutility from work



substitute consumption:

Households' optimal condition

Maximized utility function:



When functions are given, Labor Supply (L^S) can be derived from this equation.

Aggregate demand

Y = C + I + G
whereby Y is output, C is consumption, I is investment and G is government spending