How much real investment is optimal when borrowing and lending are available?
Choose investment by NPV first, then use capital markets to time consumption.
Follow the cause and effect
Write NPV(I)=−I+F(I)/(1+r).
Invest while F′(I)>1+r, subject to constraints.
Use post-investment wealth to solve intertemporal consumption.
The model you are using
Conditions for this model
Divisible project F=4√I, r=0, y₁=20,y₂=0, unrestricted credit and no risk.
The exam trap
A positive gross payoff is insufficient; compare marginal payoff with 1+r or NPV.
Connect the reasoning to the graph
What changes
- The production opportunity frontier meets the capital-market line at slope −(1+r) before consumption is chosen.
What stays fixed
Divisible project F=4√I, r=0, y₁=20,y₂=0, unrestricted credit and no risk.
Keep these conditions throughout the comparison; change only what the case above specifies.
What to inspect
Use post-investment wealth to solve intertemporal consumption.
Compare before and after, and locate the conclusion on the graph.
5 MINUTES · TRANSFER THE IDEA
Can you explain it without the lesson?
Compare two one-year projects by NPV after r rises and explain why long-duration projects are sensitive.