Briefly outline the difference between diminishing returns to a factor and decreasing returns to scale

Diminishing returns to a factor is the return from a shift in one factor or more production factors while keeping some other factors constant. The law of diminishing returns states that as production factors gradually get added, the return levels will increase but decrease eventually. On the other hand, the decreasing returns to scale occur when there is an increase in the general inputs but leads to a lesser than a proportional output increase. For example, if a shoe factory increases its variable inputs by 40% but realizes an output of 29%, a decreasing return of scale has happened.

Yes, either of the situations indicates production inefficiency. The addition of production factors creates an inefficient combination of variable and fixed production factors in the diminishing returns to a factor. Also, decreasing returns to scale, attaining lesser returns than the inputs used in the output production, indicates inefficiently used resources and input.