# Recursive Competitive Equilibrium (RCE)

## What Is Recursive Competitive Equilibrium (RCE)?

The term recursive competitive equilibrium (RCE) refers to a concept used to explore and study economic issues when supply and demand are equal. Recursive competitive equilibrium is a mathematical optimization method commonly used in macroeconomics and is characterized by time-invariant equilibrium decision rules that specify actions as a function of a limited number of variables.

RCE helps analysts and economists explore a variety of issues, such as monetary and fiscal policy and business cycle fluctuations.

### Key Takeaways

• Recursive competitive equilibrium is an equilibrium concept used to explore and study economic issues.
• It is generally used in macroeconomics, which is the broader study of the economy.
• RCE is characterized by time-invariant equilibrium decision rules that specify actions as a function of a limited number of variables.
• The assumption with RCE is that all the variables involved are current, which means that previous information available in the economy is known.
• RCE looks at what effect the functions, prices, value, and period allocation policies have on information on the economy.

## How Recursive Competitive Equilibrium (RCE) Works

Recursive competitive equilibrium is an optimization concept characterized by time-invariant equilibrium decision rules within the economy. These rules outline actions as a function of a limited number of variables. These variables, which are commonly referred to as state variables, sum up how past decisions and current information are affected.

The assumption with RCE is that all the variables involved are current. Therefore, previous information available in the economy is known. The decision rules for RCE include a number of functions, which include:

• A pricing function
• A value function
• A period allocation policy outlining the decision made by the consumer
• A period allocation policy outlining the decision made by every firm
• A function that outlines the law of motion of the capital stock

As such, RCE basically looks 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, including policies enacted by financial authorities (notably fiscal and monetary policy), as well as changes within the business cycle. Their actions will determine, in part, the values of the variables in the next sequential time period. This makes the structure recursive.

An economic agent is a consumer, corporation, or organization that makes an impact on the economy by buying, selling, or producing.

## Special Considerations

The RCE approach assumes that the consumer makes all consumption decisions, while a finite number of firms produce two goods—a consumable one and a capital one. These firms are able to 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 their wages to buy goods from firms and the process starts over each period. During this period, firms don't retain their assets (because they're sold) and technology is freely available. Some RCE models actually assume an infinite-life, maximizing value firm.

The RCE model assumes a stationary environment when it comes to finding optimal growth. The assumption is that the issue does not change with time, hence the recursive representation. Recursive problems are solved regardless of time, where a sequential model solution depends on the time period for which you're solving.

RCE allows analysts to focus on other structures of the problem. The variables are predetermined and matter. They must, therefore, vary across time and state.

The recursive competitive theory was developed by Rajnish Mehra and Edward Prescott.

## Recursive Competitive Equilibrium (RCE) and Macroeconomics

As mentioned above, recursive competitive equilibrium falls under the study of macroeconomics. This is the study of the broader economy. 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.

Economic equilibrium occurs when economic forces are balanced, which is also known as supply equaling demand. In a competitive equilibrium like RCE, supply equals demand. The RCE helps economists determine the reasons for short-term fluctuations in the business cycle and longer-term reasons for economic growth.

Article Sources
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1. National Bureau of Economic Research. "Recursive Competitive Equilibrium," Page 6. Accessed May 25, 2021.

2. National Bureau of Economic Research. "Recursive Competitive Equilibrium," Page 4. Accessed May 25, 2021.

3. National Bureau of Economic Research. "Recursive Competitive Equilibrium," Page 7. Accessed May 25, 2021.