Final answer:
Total factor productivity influences the real interest rate differently in open and closed economies, with open economies being more susceptible to changes in interest rate due to cross-border capital flows.
Step-by-step explanation:
An increase in total factor productivity affects an open economy differently from a closed economy, primarily due to how the real interest rate responds to the changes in productivity within the different economic systems. In a closed economy, the real interest rate tends to stay the same because there are no external influences to alter it, whereas in an open economy, the real interest rate can change as capital flows freely across borders in response to differing rates of return.
Productivity improvements stem from advances in human and physical capital, technology, and efficient market interactions, all of which contribute to economic growth. Such improvements lead to higher GDP per capita if accompanied by complementary increases in capital.
Concerning the options given, choices (a), (b), and (e) discuss changes in the real interest rate, while choice (c) deals with income effects, and choice (d) mentions a substitution effect in the open economy.