(b) “Homothetic production function includes Homogeneous production function as a special case.” Justify this statement.

In microeconomic analysis, production functions play a fundamental role in understanding how inputs are transformed into outputs. One of the key classifications of production functions involves homothetic and homogeneous functions. The statement "Homothetic production function includes Homogeneous production function as a special case" implies a relationship where homogeneous production functions are a subset of homothetic ones. To justify this statement, we need to explore the definitions, properties, and connections between homothetic and homogeneous production functions, and how one can be viewed as a special case of the other.

### Homogeneous Production Functions

A production function is considered homogeneous of degree \( n \) if, when all inputs are scaled by a common factor, the output is scaled by a factor of \( n \). Formally, a production function \( f(x_1, x_2, ..., x_n) \) is homogeneous of degree \( n \) if:

\[
f(t \cdot x_1, t \cdot x_2, ..., t \cdot x_n) = t^n \cdot f(x_1, x_2, ..., x_n)
\]

where \( t \) is a scalar factor and \( x_1, x_2, ..., x_n \) represent the inputs. This property indicates that if the quantity of all inputs is increased by a factor of \( t \), the output will increase by a factor of \( t^n \). 

In economic terms, a homogeneous production function of degree 1 (also known as a linear homogeneous production function) implies constant returns to scale. If \( n _____ ______ __________ ________ ______ ____.
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