GrowthAs

Syntax

GrowthAs(BranchName) or
GrowthAs(BranchName, Elasticity) or

Description

Calculates a value in any given year using the previous value of the current branch and the rate of growth in another named branch. This is equivalent to the formula:

Current Value(t) = Current Value(t-1) * NamedBranchValue(t)
NamedBranchValue(t-1)

In the second form of the function, the calculated growth rate is adjusted to reflect an elasticity. More precisely, the change in the current (dependent) branch is related to the change in the named branch raised to the power of the elasticity. This is a common approach in econometric modeling, in which the growth in one variable is estimated as a function of the growth in another (independent) variable.

Current Value(t) = Current Value(t-1) * ( (NamedBranchValue(t) / NamedBranchValue(t-1)) ^ Elasticity )

Examples

GrowthAs(Household\Rural)

GrowthAs(GDP, 1)

In this example (elasticity = 1), the current branch grows at the same rate as the named branch (GDP). When GDP doubles, so does the current branch. This is equivalent to GrowthAs(GDP) without the elasticity parameter.

GrowthAs(GDP, 0.9)

In this example (elasticity = 0.9), the current branch grows more slowly than GDP.

GrowthAs(GDP, 1.2)

In this example (elasticity = 1.2), the current branch grows more rapidly than GDP.

GrowthAs(GDP, 0)

In this example (elasticity = 0), the current branch is constant (i.e. independent of GDP).

Determining the value for Elasticity

To derive the elasticity, substitute your assumptions into the equation above. Suppose you think that demand will decrease by 25% as the price of water doubles. (This is an inverse relationship--as one increases, the other decreases--and will have an elasticity less than 0.) The expression for demand (the "water intensity" variable) will be

GrowthAs(\Key Assumptions\Price of Water, elasticity).

(This assumes that you had created a Key Assumption variable called Price of Water, and had specified the current and future values of the price. WEAP will not do this for you.)

To derive the elasticity, let's use our assumptions. NamedBranchValue doubles:

NamedBranchValue(t) = 2 * NamedBranchValue(t-1)

Current Value decreases by 25%:

Current Value(t) = 0.75 * Current Value(t-1)

Using the definition of GrowthAs with elasticity

Current Value(t) = Current Value(t-1) * ( (NamedBranchValue(t) / NamedBranchValue(t-1)) ^ Elasticity )

substitute our assumptions:

0.75 * Current Value(t-1) = Current Value(t-1) * ( (2 * NamedBranchValue(t-1) / NamedBranchValue(t-1)) ^ Elasticity )

Simplifying:

0.75 = 2 ^ Elasticity

Take the log base 2 of each side:

Elasticity = log2(0.75) = -0.415

Therefore, the expression to use for the water intensity would be GrowthAs(\Key Assumptions\Price of Water, -0.415)

In modeling demand, in addition to looking at the price elasticity of demand (demand decreases as price increases), you might also want to explore the income elasticity of demand (demand increases as income or GDP increases). For more information on elasticities, consult a basic economics textbook.