Isoquant, its Assumptions and Properties

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Isoqunat:
In Latin, "iso" means equal and "quant" refers to quantity. This translates to "equal quantity".
It is defined as the locus of points of all possible input combinations of two points x₁ and x₂ which gives same output.
qo = f (x₁, x₂), where q^o = fixed quantity.

 We can find infinite combinations in this curve with same output.
Assumptions of Isoquant curve:
1. There are only two inputs x₁ and x₂.
2. x₁ and x₂ can be substituted for one another at a diminishing rate.
3. Technology is fixed for a given period.
4. Production function is continuous i.e. x₁ and x₂ are perfectly divisible.

Properties of IQC:
1. Isoquants have a negative slope that is the curve is downward to the right.
2. Isoquants are convex to the origin.
3. Isoquants cannot intersect or be tangent to each other.
4. Higher IQC's represents a higher level of output than the lower ones.

How to construct Isoquant curve?
Let a PE q^o= x₁α. x₂α, o<α<1
∴

Now putting different values of x₁ & x₂, IQC can be drawn.
For example, when α = 1/2, IQC = ?

Source:
1. Class Note
2. Investopedia