At the point of equilibrium, IC must be convex to the origin. Why?

Ria,

The Indifference curve must be convex to the origin for a consumer to attain equilibrium because the convex shape of Indifference curve implies falling marginal rate of substitution which is necessary to attain for a consumer to attain maximum satisfaction, and hence, equilibrium.  

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It is due to dimishing MRS ( marginal rate of substitution) is decrease.
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