The 'long run' is an analytical timeframe in economics where variables that were held constant (exogenous) in the short run are allowed to become endogenous, meaning they can be adjusted and are determined by the model. The analysis of a long-run equilibrium involves modeling the consequences of these adjustments. This concept does not describe a specific period of time but rather a modeling approach where a firm can adjust all its inputs, including its capital goods.

Long Run in Economics

An endogenous variable in an economic model is one whose value is determined by the internal workings of the model itself. It is the outcome or result that the model seeks to explain. The transition from a short-run to a long-run analysis involves allowing previously fixed variables to become endogenous, meaning they can be adjusted within the model.

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A production function is a graphical or mathematical expression that represents a specific technology. It describes the relationship between the quantity of inputs used in a production process and the maximum amount of output that can be produced. For instance, in an agricultural setting with a fixed amount of land, a production function can be plotted as a graph or written as a formula showing how the total grain output changes as the number of farmers (labor input) varies.

Production Function

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To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

CORE Econ - The Economy 2.0: Microeconomics

To analyze how grain production changes with the number of farmers, data can be presented in a table. This table typically lists various levels of labor input (number of farmers) and the corresponding total grain output. A third column is often included to display the calculated average product of labor for each input level, which helps illustrate how productivity changes as labor input varies.

Tabulated Data for a Farmer's Production Function

Jean Baptiste Tavernier, a French diamond merchant from the seventeenth century, is a key historical source on economic conditions due to his extensive travels. His writings are particularly notable because they echo the sentiments of Ibn Battuta regarding the abundance in Bengal, providing corroborating testimony three centuries after the Moroccan scholar's visit.

Jean Baptiste Tavernier

The average product of an input is a measure of its productivity, calculated by dividing the total output by the total quantity of that specific input. For example, the average product of labor (APL), also known as labor productivity, is found by dividing the total output, `y`, by the total labor input used in production.

Average Product of an Input

The graphical representation of a farmer's production function for grain shows how output changes with labor input, assuming specific conditions such as average growing conditions and the use of currently available technology. The graph plots the number of farmers (from 0 to 2,800) on the horizontal axis against the grain output in thousands of kilograms (from 0 to 1,000) on the vertical axis. This production function is depicted as an upward-sloping, concave curve starting at the origin and passing through points like A (800, 504) and B (1,600, 778), visually demonstrating how total grain production is affected by the number of farmers employed under these fixed conditions.

Graphical Representation of the Farmers' Production Function for Grain

The mathematical form of a production function can be simplified to Y = f(X) when all inputs except one are held constant. In this equation, 'X' represents the quantity of the single variable input, such as the number of farmers, while 'Y' is the total output, like grain produced. The function f(X) details the specific relationship, which can be visualized as a curve, showing how output responds to changes in the variable input, assuming other factors like land are fixed.

Mathematical Expression of a Production Function with One Variable Input: Y = f(X)

The 'Introduction to Mathematical Extensions' provides foundational context for the mathematical techniques used in the course. It offers a brief explanation of calculus and outlines the specific mathematical level, notation, and conventions that are followed in the analyses.

Introduction to Mathematical Extensions for Economic Analysis

The technology for modern olive oil production can be modeled by a production function with two primary inputs: labor (number of workers, $N$) and energy ($E$). This simplification is possible due to the assumption that capital and energy are used in fixed proportions. This specific production technology also exhibits constant returns to scale, meaning that if both labor and energy inputs are increased by a certain percentage, the output of olive oil increases by the same percentage. The model deliberately omits raw materials, assuming the required quantity of olives is determined by the production target.

Production Function for Olive Oil with Two Variable Inputs and Constant Returns to Scale

In economic analysis, it is common to model scenarios where some inputs are held constant because many factors of production, such as land, premises, or machinery, are difficult to adjust quickly. This approach is frequently used to study how output is affected by varying a more flexible input, like labor, while the other factors remain fixed.

Variability in the Adjustability of Factors of Production

A specific olive oil producer's technology can be described by the Cobb-Douglas production function: $Y = 0.5E^{0.8}N^{0.4}$. In this model, $Y$ represents the total output of olive oil, $E$ is the quantity of energy used, and $N$ is the number of workers employed. The text also proposes analyzing a scenario where the energy input $E$ is held constant at 100 units.

A Cobb-Douglas Production Function for an Olive Oil Firm

A firm's cost function, often represented as C(Q), describes the relationship between its total costs and its level of output (Q). This function determines the total expenditure, including the opportunity cost of capital, required to produce a specific quantity of goods or services. It is a fundamental tool for analyzing a firm's decisions regarding production levels and pricing.

Firm's Cost Function

An exogenous variable in an economic model is one whose value is determined outside the model. Its value is set by the modeler and is taken as a given, rather than being explained by the model's internal mechanics. In short-run analysis, variables that are difficult to adjust, such as capital stock, are often treated as exogenous.

Exogenous Variable

Endogenous Variable

The differentiation between the short run and the long run is a common and useful framework in many economic models. [3] This distinction is particularly helpful in situations where certain economic variables can only adjust slowly, allowing for an analysis of outcomes both before and after these factors have fully adjusted.

Short-Run vs. Long-Run Analytical Framework

A dataset, referenced as Figure 8.13a, which provides data on the production of quinoa.

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