Q. Show the Properties of isoquants?

Isoquants slope downwards to the right:  It means that, in order to keep output constant; when amount of one factor is increased then the quantity of other factor should be decreased.

An upward sloping isoquant illustrates that a given product can be produced with less of both the factors of production. An entrepreneur, who is maximising profits, wouldn't use any combinations of factors exposed on an upward sloping portion of an isoquant. Thus the points on the upward sloping portion of an isoquant can't represent an equilibrium position. In the same way, a horizontal or vertical range of an isoquant cannot also represent a possible position of equilibrium. In this circumstance, the same output could be attained at a reduced cost by decreasing the amount of one of the factors. So isoquants slope downwards to the right as in figure below.

Figure: Isoquant sloping downwards