# Short Run vs Long Run Cost Functions

Let $z_a$ and $z_b$ are two vectors of inputs. $z_a$ is variable in both long run and short run however $z_b$ is only variable in long run.

Now let's suppose that the price of one of the inputs in vector $z_a$ increases (let's say $z_a^i$), how would that effect the marginal cost in the long and short run? Can we compare the long run and short run marginal cost because of this price change?

I understand the relationship of long run and short run costs and marginal costs, however I am finding a hard time understanding these price change effects. Any help is appreciated.