page_title: Robinson Crusoe economy
section_title: Production function and indifference curves
hierarchical_section_title: Robinson Crusoe economy / Production function and indifference curves
caption_attribution_description: English: The Robinson Crusoe Economy's Production Function and Indifference Curves
context_page_description: A Robinson Crusoe economy is a simple framework used to study some fundamental issues in economics. It assumes an economy with one consumer, one producer and two goods. The title "Robinson Crusoe" is a reference to the 1719 novel of the same name authored by Daniel Defoe.
  As a thought experiment in economics, many international trade economists have found this simplified and idealized version of the story important due to its ability to simplify the complexities of the real world. The implicit assumption is that the study of a one agent economy will provide useful insights into the functioning of a real world economy with many economic agents. In other fields of economics, the Robinson Crusoe economy framework is used for essentially the same thing. For example, in public finance the Robinson Crusoe economy is used to study the various types of public goods and certain aspects of collective benefits. It is used in growth economics to develop growth models for underdeveloped or developing countries to embark upon a steady growth path using techniques of savings and investment.
context_section_description: Crusoe's indifference curves depict his preferences for leisure and coconuts while the production function depicts the technological relationship between how much he works and how many coconuts he gathers. If the axes depicting coconut collection and leisure are reversed and plotted with Crusoe's indifference map and production function, figure 2 can be drawn:
  The production function is concave in two dimensions and quasi-convex in three dimensions. This means that the longer Robinson works, the more coconuts he will be able to gather. But due to diminishing marginal returns of labour, the additional number of coconuts he gets from every additional hour of labour is declining.
  The point at which Crusoe will reach an equilibrium between the number of hours he works and relaxes can be found out when the highest indifference curve is tangent to the production function. This will be Crusoe's most preferred point provided the technology constraint is given and cannot be changed. At this equilibrium point, the slope of the highest indifference curve must equal the slope of the production function.
  Recall that the marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility. Additionally, an input's marginal product  is the extra output that can be produced by using one more unit of the input, assuming that the quantities of no other inputs to production change. Then,
  MPL = MRSLeisure, Coconuts
  where
  MPL = marginal product of labour, and
  MRSLeisure, Coconuts = marginal rate of substitution between leisure and coconuts
caption: Figure 2: The Robinson Crusoe economy's production function and indifference curves
exif: {}