q 3. )
We have 3 cases:
alpha>1 indifference curve is concave so extremes are preferred
alpha =1, perfect substitute , so extremes are preferred'
alpha<1, indifference curve is convex so means are preferred
but if we simply substitute the budget constrant into the function and maximize alpha gets cancelled out and we aRE LEFT WITH CONVEx PREFERENCES DEMAnD FUNCTIONs why is that happening
Case 1 - (alpha<1)
Indifference curves are convex shaped. And since both goods get equal weights and prices are equal, x=y=(M/2p)
Case 2 - (alpha=1)
Perfect substitutes case. So any combination of x and y satisfying x+y=M
Case 3 - (alpha>1)
Indifference curves are concave to the origin (if that's the right terminology). And the indifference curve touches the budget line at the x and y axes. So either x=(M/p) or y=(M/p)