Amartya Sen was awarded the Nobel Prize for his contribution to Welfare Economics. Welfare economics is a branch of economics that focuses on the well-being and welfare of individuals and society as a whole. It involves the study of how resources are allocated and distributed in order to maximize social welfare.

Option 1, Monetary Economics, deals with the study of money, banking, and the monetary policies of a country. While Sen has made significant contributions to the field of economics, his work does not particularly focus on monetary factors.

Option 3, Environmental Economics, is concerned with the economic impact of environmental policies and the valuation of natural resources. Sen`s work may touch on environmental factors indirectly in relation to social welfare, but it is not the primary focus of his contributions.

Option 4, Development Economics, is the study of how economies grow and develop, particularly in low-income countries. Sen has indeed made valuable contributions to development economics, including his work on poverty, social inequality, and capabilities approach, which focuses on the ability of individuals to function in society. However, specifically, he was awarded the Nobel Prize for his contributions to welfare economics.