Step 1: Understand investment in the economy.
In national income accounting, investment is the expenditure on new capital goods that increase the economyβs productive capacity. Buying an existing house is considered consumption, not investment, since no new production occurs.
Step 2: Analyze the cases.
- Rosy buying a 50-year-old house is considered consumption, not investment, as the house is already built and no new capital is created.
- Cathy building a new house for herself is considered investment because it is the construction of new capital.
Thus, the total investment in the economy is only the new house Cathy builds, which counts as 1 house.
Final Answer:
\[
\boxed{1 \text{ house}}
\]