Step 1: Understand the question.
The question asks who won the 2024 Nobel Prize in Economic Sciences for studies on how institutions are formed and affect prosperity.
Step 2: Examine each option.
- Option A: Correct. Daron Acemoglu, Simon Johnson, and James A. Robinson are recognized for their work on the role of institutions in economic growth and prosperity.
- Option B: Claudia Goldin won the prize in 2022 for gender economics, not in 2024.
- Option C: Ben Bernanke, Douglas Diamond, and Phillip Dybvig won the Nobel in 2022 for their work on financial institutions.
- Option D: Paul Milgrom and Robert Wilson won the Nobel in 2020 for auction theory, not related to institutions.
- Option E: David Card, Joshua Angrist, and Guido Imbens received the 2021 prize for their contributions to labor economics and causal inference.
Step 3: Conclude.
The correct answer is Daron Acemoglu, Simon Johnson & James A. Robinson.
Final Answer:
\[
\boxed{\text{A}}
\]