The total fertility rate in an economy is defined as:

The correct option is: the average number of live births a woman would have by the end of her child-bearing age.

Explanation:
The Total Fertility Rate (TFR) is a key demographic metric used to measure the fertility of a population. It represents the average number of children that would be born alive to a woman during her lifetime if she were to pass through her child-bearing years (typically defined as ages 15 to 49) conforming to the age-specific fertility rates of a given year.

To understand why this is the correct definition, let's distinguish it from the other options:
1. Crude Birth Rate: The number of children born per 1000 people in the population in a year is the definition of the Crude Birth Rate (CBR). Unlike TFR, which focuses strictly on the cohort of women in their reproductive years, CBR relates births to the entire population (including males, children, and post-reproductive individuals).
2. Rate of Natural Increase: The birth rate minus the death rate is the rate of natural increase (or natural growth rate) of a population, which reflects the pace at which a population grows or shrinks due to biological factors (excluding migration).
3. Couples vs. Cohorts: The total fertility rate is a statistical projection representing the average experience of a woman across the entire population, rather than a measure restricted to couples.

Therefore, the total fertility rate is properly defined as the average number of live births a woman is expected to have by the end of her child-bearing age.