Monday, December 21, 2009

A Stimulus That Could Save Money

New York Times article A Stimulus That Could Save Money (November 17th, 2009) cites a McKinsey & Company report that neglects the most fundamental economic thinking to argue that increasing home efficiency will reduce energy use.

The bottom line is that cash for caulkers would be trickier than cash for clunkers — yet would have the potential to do far more good. McKinsey, the consulting firm, estimates that households could reduce their energy use by 28 percent over the next decade. In terms of greenhouse gases, that would be the equivalent of taking half of all vehicles in this country off the road.

Corrections notes that far from decreasing energy use, the sign of an impact of increased efficiency on energy use is indeterminate. People don't want energy as an end consumable product; energy is purchased as an input into producing heat, light, or other consumable amenities. The real product they are purchasing, then, is heat and light. Therefore, we can write the "price" of a unit of heat as the price of electricity multiplied by how much electricity is required per unit of heat.

Therefore, we can see that a doubling of energy efficiency (halving the number of units of electricity per unit of light) is the same as halving the price of electricity. In other words, we may think of this "cash for caulkers" idea as reducing the effective price of light.

This is the point at which McKinsey & Company's analysis stops. They examine energy use as "business-as-usual", assuming "no material change in consumer utility or lifestyle preferences" (page 23 of the above report). Using our above analysis, we can say it is ludicrous to say that light use will remain the same if the price of electricity for light is reduced. As light is a normal good, we will observe light use increasing as price decreases. The remaining question is whether or not, when we halve the "price" of light, energy consumption more than doubles or not. If it increases by a factor greater than two, we should see energy use increasing.

The New York Times took McKinsey's mistaken assumption that consumption of light and heat would remain the same in the face of a decrease in their effective price, and concluded that the price of energy may decrease. In fact, from the Slutsky identity, it can be easy for energy use to increase, given that light and heat are normal goods, and the share of income spent on them is not low.  The possibility for the consumption of light to more than double after efficiency is doubled is depicted graphically below (click to enlarge), along with the possibility for it to increase by less than a factor of two.

Mathematically, the percentage change in heat consumption given a percent change in the effective price of heat will be determined by the Hicksian Elasticity of substitution (negative), the share of income spent on heat consumption and the income elasticity of heat (greater than zero). If our LHS is less than negative one, we will see our predicted increase in energy consumption.

As a final point, we can add that we expect energy companies, as monopolies, to be pricing on the elastic part of the demand curve for energy in general. Monopolies never price on the inelastic portion of a demand curve. To the point that prices are set by the government for energy companies, it is important to note that the more inelastic price is, the more companies have an incentive to lobby and change price, and our suggestion that energy should already be priced on the elastic portion of the demand curve remains intact.

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