It is likely that there will be a corner point solution when
a) two goods are perfect substitutes and the marginal rate of substitution is equal in magnitude to
the slope of the budget constraint. it happens because when two goods are perfect substitutes the consumer doesnot go for joint consumption which generally a case of complementary goods. here the consumer goes for one single commodity which results in a cornor solution. here consumer preference is (x,0) or (0,y). it cant be both at the same time.
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