Robinson Crusoe economy
A Robinson Crusoe economy is a simple framework used to study some fundamental issues in economics.
In other fields of economics, the Robinson Crusoe economy framework is used for essentially the same thing.
[1] Similar to the choices that households (suppliers of labour) face, Crusoe has only two activities to participate in – earn income or pass his time in leisure.
If the axes depicting coconut collection and leisure are reversed and plotted with Crusoe's indifference map and production function,[1] figure 2 can be drawn: The production function is concave in two dimensions and quasi-convex in three dimensions.
[1] 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.
The firm will want to maximise profits by deciding how much labour to hire and how many coconuts to produce according to their prices.
[5] Let's assume that a currency called "Dollars" has been created by Robinson to manage his finances.
This assumption is made to make the calculations in the numerical example easy because the inclusion of prices will not alter the result of the analysis.
Then, The above function describes iso-profit lines (the locus of combinations between labour and coconuts that produce a constant profit of Π).
[1] The vertical intercept of the iso-profit line measures the level of profit that Robinson Crusoe's firm will make.
The distance from L' to the chosen supply of labour (L*) gives Crusoe's demand for leisure.
Given the wage rate, Crusoe will choose how much to work and how much to consume at that point where, At equilibrium, the demand for coconuts will equal the supply of coconuts and the demand for labour will equal the supply of labour.
In other words, using the market system has the same outcome as choosing the individual utility maximisation and cost minimisation plans.
[1] This is an important result when put into a macro level perspective because it implies that there exists a set of prices for inputs and outputs in the economy such that the profit-maximising behaviour of firms along with the utility-maximizing actions of individuals results in the demand for each good equaling the supply in all markets.
Now, Robinson has to decide how much time to spare for both activities, i.e. how many coconuts to gather and how many fish to hunt.
[1] The locus of the various combinations of fish and coconuts that he can produce from devoting different amounts of time to each activity is known as the production possibilities set.
[9] This is depicted in the figure 6: The boundary of the production possibilities set is known as the production-possibility frontier (PPF).
[9] This curve measures the feasible outputs that Crusoe can produce, with a fixed technological constraint and given amount of resources.
In figure 6, the underlying assumption is the usual decreasing returns to scale, due to which the PPF is concave to the origin.
In case we assumed increasing returns to scale, say if Crusoe embarked upon a mass production movement and hence faced decreasing costs, the PPF would be convex to the origin.
The MRT is thus, Under this section, the possibility of trade is introduced by adding another person to the economy.
Suppose that the new worker who is added to the Robinson Crusoe economy has different skills in gathering coconuts and hunting fish.
If he too decides to work for 12 hours, his production possibilities set will be determined by the following relations: Thus, MRT Coconuts, Fish
Their respective PPFs can be shown in the following diagram: The joint production possibilities set at the extreme right shows the total amount of both commodities that can be produced by Crusoe and Friday together.
[1] In a simple exchange economy, the contract curve describes the set of bundles that exhaust the gains from trade.
[5] From the figure 8, it is clear that an economy operating at a position where the MRS of either Crusoe or Friday is not equal to the MRT between coconuts and fish cannot be Pareto efficient.
