Why $\gamma(c,i)=cv(i)$ means diseconomies of scale?

Question

Let's define the transaction cost of credit consumption as $\gamma(c,i)$ where $c$ is consumption and $i$ is a fraction of credit purchase.
If the transaction technology does not exhibit economies of scale,
it can be expressed with some function $v(\bullet)$ as: $\gamma(c,i)=cv(i)$
It means per unit cost of transating goods is independent of the volume transacted.
But in this equation $c$ is left so I wonder how can we say that "it is independent of the volume transacted".

Can anyone tell me the reason?

Answer 1

You wrote:

It means per unit cost of transating goods is independent of the volume transacted.\ But in this equation $c$ is left so I wonder how can we say that "it is independent of the volume transacted".

Therefore, it is the per unit cost that is independent of $c$, not the total cost $\gamma(c,i)=cv(i)$, which of course depends on $c$.

The per unit cost is: $$\frac{\gamma(c,i)}{c}=v(i)$$

that is evidently independent of $c$, as $v(i)$ is independent of $c$.