Massachusetts Institute of Technology This is to certify that Ashish Kumar Rai has successfully completed Microeconomics Issued: Jan. 13, 2021
Chris Capozzola

Senior Associate Dean for Open Learning

Professor of History

Massachusetts Institute of Technology

Eric Grimson

Vice President for Open Learning

Massachusetts Institute of Technology

Valid Certificate ID: 2c10a12b-f55b-d7bc-a4e8-e4828d3e15c2

© 2026 Massachusetts Institute of Technology