A Simple Economic Model of Consumer Theory

Photography from Radek Grzybowski

Dear Students,
On this Article you will find derivations of basic consumer theory and utility maximization:
  • First, we derive and simple economic model of consumer theory and show the optimal consumption choice of a single good for a single household in a closed economy setting with one firm. 
  • Secondly, the model is then extended to incorporate optimal choice of two goods in a world with a single closed economy.
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A. Economic Environment

Economics is the study of rational choice and rational allocation of scarce resources in a world, where people are faced with opportunity costs; which are the cost of a forgone opportunity at any particular point of time, where decisions are instantly made based on information available.


If we follow the assumptions;

  • that people behave rational,
  • are self-interested,
  • therefore have rational preferences choices
  • that all people have unlimited access to full information at all times
  • and that there are no transaction costs involved in searching, selection, negotiating, processing and controlling any contract (See Coase, 1960)

then we can show that economic subjects know the optimal choice rules (See Varian, 2014). In this simple Model, we reduce the analysis to the optimal choice rules of a private household (called a Consumer) and assume that Production from Firms in  this single closed economy is efficient at all levels and that the there is not need for the State to be formed. Such a model has the configuration of the form 1-Consumer-1-Firm-No-State-Model. The producer theory of firms and the collective choice theory of the State will be introduced at other stages in the respective order. In Short: In this Model there

  • is one privately consuming household in a closed economy setting
  • is one privately producing firm with no production capacity limit
  • in a closed economy setting (No trade with foreign countries)

B. Summary of Assumptions

In scientific economic analysis assumptions are means of constructing environments where human interaction, behavior and the consequences thereafter can be formally revealed. In a simple economic models the following assumptions are necessary:

  1. Economic subjects (private Households, Firms and the State) are assumed to always behave rational (Homo Oeconomicus) and are self-interested (Neoclassical Assumption). Rational behavior only holds if the subsequent assumptions are fulfilled.
  2. Economic subjects therefore have rational preferences and choice of consumption, production and redistribution of scarce resources in their economy.
  3. Economic subjects have access to symmetric full information at each point of time and their no bias in information delivery and there are no transaction costs.
  4. The economy is closed (no trade or relations with foreign countries) does not have any social planner (no state or government) for public good provision, no taxation and there is no conflict in the society. The Economy contains only two economic subjects; one privately consuming household and one privately producing firm. You can call this the garden of Eden or Robinson Crusoe Island.

Now that the economic setting of the simple model is fixed (see Varian, 2014 and others), we can proceed the describing the behavior of economic subjects.

C. Behavior of Economic Subjects

Economic models need behavioral settings that help to capture desired behavioral structures in the society. In this case we need to set the behavior of privately producing firms and the privately consuming households.

C.1 Behavior of Firms

The firm is assumed to behave as a price taker (perfect market competition, no monopoly. Further, the firm produces:



units of Goods that is consumed by the household after purchasing the good at competitive market price of:



. All income from the firm flows to the household at level:



At this point the optimal decision of the firm is supply the market with the amount demanded , if all cost of production will be fully covered by the proceeds from the sales to the household; Therefore the market clearing condition will be that the amount demanded equals the amount supplied at the time on exchange in the market.


In Short, the perfect market equilibrium is fulfilled by the market clearance condition that demand equals supply:



Where d=Index for demand and s= Index for supply.

C.2 Behavior of private Household

Coming soon.

D. Optimization Problem

Coming soon

E. First Order Conditions

Coming soon.

F. Second Order Conditions

Coming soon.

G. Opportunity Costs

Coming soon.

H. Optimal Demand

Coming soon.

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