Consider the household decision of whether to purchase a cell phone in month M. We hree-step process to produce the cell phone acquisition probability function a(M) employed in our simulation: Find historic data about the number of of cell phone owners over time Interpolate between the data points Define a(M), the probability of a simulated household acquiring a cell phone in month M For step one, we used the following data obtained from the International Telecommunication Union. In step two, we use a linear interpolation between available data points to make a con tinuous function from 1990(the start of our simulation) to 2009 Cell Phone Penetration Demographics Then, we use a linear regression to extrapolate the function between 2009 and 2040. Call this function f. Then, for step three, C(H, M) a(M)=f(M) m(H, M H∈ Houses Where c(H, M) is the number of cell phones owned by members of simulated household H in month M; and m(H, M) is the number of members in simulated household H in month M and ' is the set of all households in the simulation. In essence, Equation 3 subtracts the current simulated cell phone penetration during month M from the approximated market pene- tration,f(M), which is derived from available data Using a(M), the households in our simulation make decisions that approximate historical data As the second term in Equation 3 approaches the historical value returned by f(M), the chances of a simulated household buying a cell phone decreases to zero The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reservedConsider the household decision of whether to purchase a cell phone in month M. We use a three-step process to produce the cell phone acquisition probability function a(M) employed in our simulation: • Find historic data about the number of of cell phone owners over time. • Interpolate between the data points. • Define a(M), the probability of a simulated household acquiring a cell phone in month M. For step one, we used the following data obtained from the International Telecommunication Union. In step two, we use a linear interpolation between available data points to make a con￾tinuous function from 1990 (the start of our simulation) to 2009. 0 0.2 0.4 0.6 0.8 1 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 Percentage Year Cell Phone Penetration Demographics Figure 4. Then, we use a linear regression to extrapolate the function between 2009 and 2040. Call this function f. Then, for step three, a(M) = f(M) −   X H∈H ouses c(H, M) X H∈Houses m(H, M)   (3) Where c(H, M) is the number of cell phones owned by members of simulated household H in month M; and m(H, M) is the number of members in simulated household H in month M; and ‘Houses’ is the set of all households in the simulation. In essence, Equation 3 subtracts the current simulated cell phone penetration during month M from the approximated market pene￾tration, f(M), which is derived from available data. Using a(M), the households in our simulation make decisions that approximate historical data. As the second term in Equation 3 approaches the historical value returned by f(M), the chances of a simulated household buying a cell phone decreases to zero. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved