Recursive Competitive Equilibrium (RCE)

Recursive competitive equilibrium (RCE) is an equilibrium concept used to explore economic issues. RCE helps analysts and economists explore such issues as monetary and fiscal policy and fluctuations in the business cycle.

Recursive competitive equilibrium is a mathematical optimization method, characterized by time-invariant equilibrium decision rules that specify actions as a function of a limited number of variables.

It's assumed that all the variables are current and previous information available in the economy is known. RCE decision rules include a number of functions, such as pricing and value. Basically, looking at what effect the functions, prices, value and period allocation policies, have on the variables, which is the information on the economy. Equilibrium objects are the functions instead of variables in RCE.

Economic agents with knowledge of these variables assess the current state of the economy. Their actions will determine, in part, the values of the variables in the next sequential time period, making the structure 'recursive'.

Recursive competitive equilibrium falls under the study of the broader economy, better known as macroeconomics. Economic equilibrium is when economic forces are balanced, also known as supply equaling demand. In a competitive equilibrium like RCE, supply equals demand.

Macroeconomics involves the study of broader economic trends and indicators, such as national income, unemployment rates and Gross Domestic Product (GDP). It also studies the relationship of such economic factors as inflation, trade, consumption, and income.

The RCE helps economists determine the reasons for short-term fluctuations in the business cycle and longer-term reasons for economic growth.

The RCE approach assumes consumer make all consumption decision, while a finite number of firms produce two goods, a consumable one and a capital one, and they maximize their profit each period. It assumes firms purchase inputs and labor at competitive prices after assessing productivity at the start of the period.

Consumers then use wages to buy goods from firms and the process starts over each period, with firms not retaining assets and technology is freely available. Some RCE models do assume an infinite-life, maximizing value firm.

In finding the optimal growth, the RCE model assumes a stationary environment where the issue does not change with time, hence the recursive representation. Where a sequential model solution depends on the time you’re solving for, recursive problems are solved for regardless of time. RCE allows analysts to focus on other structures of the problem. The variables are predetermined and matter and must vary across time and state.