Effectiveness and efficiency are very much related concepts, and by that count we can say that managerial effectiveness and managerial efficiency are also closely related - However, we must note that these two terms are not used very commonly. Therefore we must have clarity about what we mean by these two terms. If we define effective manager as one who delivers results that are effective, and efficient manager as one who delivers efficient results, then we just need to understand the relationship between effectiveness and efficiency to understand the relationship between managerial effectiveness and managerial efficiency.
Effectiveness is defined as the measure of total output produced, and efficiency is defined as a ratio of output produced and input used to produce it. Thus:
Effectiveness = Output produced
Efficiency = (Output produced)/ (Inputs used)
When the inputs available for producing are being fully utilized, the output or the effectiveness's can be increased further only by increasing the efficiency. In this situation, effectiveness and efficiency are directly proportional.
In other situations it may be possible to increase output by increasing the inputs. In this case the productivity increases with increase production, but the efficiency may remain same, increase, or decrease with production depending on increase in inputs. In this case, efficiency and effectiveness are two independent variable. Fall in efficiency may or may not be compensated by benefits of increased productivity. For example, it may be possible to increase production by increasing production cost. This may be justified as long as higher profit from increased sales, more than compensates for the increased costs.
In a real life situation, some minimum efficiency is essential to compete effectively in the market. Also given same volume of sale with more efficient operations means higher profit, which in turn contributes to higher growth and higher effectiveness.
Thus we can say that in situation of resource constraints, efficiency and effectiveness are directly proportional. In absence of resource constraints efficiency and effectiveness are not necessarily related. However, in long term better efficiency contributes to improvement of higher effectiveness.