Why is the indifference curve not concave to the origin and always convex?
The indifference curve is a curve drawn with the number of units of a product A on the x-axis and number of units of another product B on the y-axis. Along the curve, the sum of the total utility obtained from different units of each of the products is the same.
Indifference curves are convex to the origin because the increase in utility from an increase of a single unit of any product does not remain the same. For example, if you may be very pleased to have two pizzas instead of one. But there would not be much of a change in how pleased you are if you could have 21 pizzas instead of 20. This is called a decrease in marginal utility and is the reason why indifference curves are convex.
As the number of any one of the products is increased to compensate for a decrease in the number of units of the other, the increase in the number of units does not remain the same but grows larger.