Concept:
The Nobel Prize in Economics recognizes important contributions to economic theory, policy, and research.
Step 1: Match Abhijit Banerjee correctly.
Abhijit Banerjee received the Nobel Prize for work related to:
\[
\text{Poverty Alleviation}
\]
Thus:
\[
A \rightarrow IV
\]
Step 2: Match Paul Krugman correctly.
Paul Krugman is known for:
\[
\text{New Trade Analysis Theory}
\]
Thus:
\[
B \rightarrow I
\]
Step 3: Match Thomas Schelling correctly.
Thomas Schelling contributed significantly to:
\[
\text{Game Theory Analysis}
\]
Thus:
\[
C \rightarrow II
\]
Step 4: Match Amartya Sen correctly.
Amartya Sen is famous for contributions to:
\[
\text{Welfare Economics}
\]
Thus:
\[
D \rightarrow III
\]
Step 5: Write the complete matching.
The correct sequence becomes:
\[
A-IV,\; B-I,\; C-II,\; D-III
\]
Step 6: Conclusion.
Therefore, the correct answer is:
\[
\boxed{A\text{-}IV,\; B\text{-}I,\; C\text{-}II,\; D\text{-}III}
\]