3.2. Question 2 Parametric cost estimates are often based on a single variable representing the capacity or some physical measure of the design, such as floor area in buildings, length of highways, volume of storage bins and production volumes of processing plants. Costs do not always vary linearly with respect to different facility sizes. Typically, scale economies or diseconomies exist. If the average cost per unit of capacity is declining, then scale economies exist. Conversely, scale diseconomies exist if average costs increase with greater size. Empirical data are sought to establish the economies of scale for various types of facilities if they exist, in order to take advantage of lower costs per unit of capacity. Three example relationships are shown below. Y .'r' I y=a+bx y=ax\" [U'D'H yzax' {Dell 3 l' '3 d X X {a} Linear Cost Relationship (bi Increase Return to Scale {0) Decreasing Return to Scale with Economies of Scale y=a+bx y=axb(01) 1ny=lna+blnx x: a certain range of the variable x (e. ,9- . floor area) 1 l + b1 11 y = n yn 11:: y: the cost of a facility corresponding to any x A nonlinear cost relationship often used in estimating the cost of a new industrial processing plant from the known cost of an existing facility of a different size is known as the exponential rule (as shown below). Q 3* = xiii)m TI y\": known cost of an existing facility with capacity Q; )1: estimated cost of the new facility with capacity Q Empirical cost data from a number of sewage treatment plants are plotted below in Figure 1. Determine the cost exponent m based on the empirical data. Discuss how much cost is to be increased when the capacity of a plant is doubled. log 0.2 (0.301, 0.176) 0.1 O log O 0.1 0.2 0.3 0.4 Qn Figure 1: Log-Log Scale Graph of Cost Data from Sewage Treatment Plants