Final answer:
The Fisher separation theorem is graphed by plotting the initial endowment, optimal production, and optimal consumption, illustrating how individuals can separate their consumption preferences from investment decisions. In the case of borrowing, the individual's consumption point moves beyond their production possibilities frontier due to additional capital obtained through a loan.
Step-by-step explanation:
The student's question deals with the graphical demonstration of the Fisher separation theorem, particularly in a scenario where an individual borrows in the capital market.
The Fisher separation theorem helps us understand that investment decisions are separate from the preferences of individual consumers and producers, implying that the firm's choice of investments can be made independently of the owners' consumption preferences.
Graphical Demonstration
To illustrate the Fisher separation theorem graphically, we begin by plotting the individual's initial endowment, which is represented as point (Y₁, Y₂) on the graph. This point reflects the individual's initial financial resources or wealth in two different time periods. Next, we plot the optimal production/investment point (P₁, P₂), which is determined by the production possibilities frontier of the individual or firm. This frontier represents the maximum possible output that an individual or firm can produce with the available resources.
Alongside the production possibilities frontier, we draw the individual's budget constraint, which reflects the various combinations of present and future consumption that the individual can afford given their initial endowment and prevailing interest rates.
The point where the budget line is tangent to the production possibilities frontier is the optimal consumption point (C₁, C₂). This is where the marginal rate of transformation between present and future goods in production equals the marginal rate of substitution between present and future goods in consumption, adjusted for interest rates.
If an individual ends up borrowing, it means that they move from their initial endowment to a consumption point that lies beyond their production possibilities frontier. This can occur because they can loan additional financial capital from the market, allowing for higher present consumption, C₁, at the expense of future consumption, C₂. On our graph, the budget line will shift outwards, representing the extended possibilities from borrowing.