In the above expression C1 and C2 are the costs at the same point in time, at which the estimate is required. Both Q1 and Q2 are in same physical units. The power-sizing exponent ‘x' represents the economies of scale. The economies of scale indicate that the cost per unit output decreases as the size of operation increases. The decrease in cost per unit output occurs as the fixed cost is distributed over more number of output units as the scale of output increases and in addition the efficiency grows in production with increasing size of operation. Taking a simple example, the cost of constructing a four-storey hostel building will normally be less than twice the cost of constructing a similar two-storey hostel building. One of the factors that gives rise to cost advantage in case of four-storey building is the cost of land (fixed cost), which is same for both buildings.
If the value of power-sizing exponent ‘x' is less than 1, it indicates economies of scale whereas greater than 1 indicates diseconomies of scale. When the value of power-sizing exponent is equal to 1, it indicates a linear relationship between cost and capacity or size.
While using this technique to predict the current cost of an industrial plant of a given capacity (Q1) from known past cost of the same plant of a different capacity (Q2), first it is required to update the known past cost of the plant with capacity (Q2) to the present time by using the relationship for cost index (as stated in previous lecture) from the known values of cost indexes in past and in current time. After that, the cost of the plant with capacity Q1 is estimated using the power-sizing model (as stated above) from the updated cost of plant with capacity Q2 (i.e. cost at current time) and value of the power-sizing exponent for this particular plant.
Learning curve is also another cost estimating relationship and it is based on the principle that with increase in number of repetitions, the performance becomes faster with increase in efficiency. In other words the time or cost of producing a unit output of a product/system reduces, each time it is produced. Learning curve relates to improvement in performance with increase in repetitions. A learning curve model is based on the assumption that, the time to produce a unit output reduces by a constant percentage as the number output unit is doubled. The reduction in time depends on the learning curve rate. Taking a simple example, if the time required to complete the production of first output unit is 20 hours, then the time required to complete the production of the second output unit at 80% learning curve rate will be 16 hours (20 hours x 0.80). This 80% learning curve rate indicates a 20% reduction in production duration, each time the output is doubled Similarly the time required to produce the fourth output unit will be 12.8 hours (16 hours x 0.80). The reduction in production time for fourth unit as compared to the second unit is 3.2 hours (16 hours – 12.8 hours) which is 20% of production time for the second output unit.