Income elasticities for environmental goods
Conventionally estimated income elasticities for environmental goods often appear to be less than 1.0.  This seems counter intuitive, and at odds with causal observation and introspection.  It seemsmore likely that income elasticity of demand for environmental preservation such as agricultural landscapes, wildlife amenity benefits, and the separation of towns by green belts, etc. might be greater than one - the richer we are the more important these things become. 

The argument can be developed (without loss of generality) using a simple linear demand for an environmental good expressed as:
Q  =  a + bP + cY
where Q = quantity demanded; P = price; and Y = income. 

The respective price and income elasticities (e andh respectively) for this linear demand function are
e  =  b*(P/Q)        and         h  =  c*(Y/Q)

The value of an environmental good is typically estimated through CVM in terms of the willingness-to-pay (WTP) for the good, so the relationship of interest is the price dependent demand function:
P  =  [Q - a - cY] / b

From this price dependent equation, the "income flexibility", as a proportionate change in the price (willingness to pay ) per proportionate change in income is defined as:
∂P/∂Y * (Y/P)  =  (-c/b)*Y/P

This is the measure that is intuitively grasped when considering the effect of income on the demand for an environmental good.  It is this measure that should be considered in the case of a public good, since for any individual the quantity of a public good is not a control variable: it is fixed by public or collective action.  Furthermore, in the case of many environmental goods, the total supply is frequently strictly limited.  

In this linear case (and more generally), therefore, the relationship between income flexibility for an environmental good and the conventional income elasticity is as follows:
∂P/∂Y * (Y/P) =  (-c/b)*Y/P  =  [c*(Y/Q)] / [-b*(P/Q)]  =  h / -e

Thus, although the income elasticities for public goods are often measured as less than 1.0, so long as the corresponding price elasticity is less in absolute terms than this income elasticity, the income flexibility (as the increase in the willingness to pay per proportionate increase for the public good is greater than 1.0.  It seems intuitive that the price elasticity of demand for environmental public goods may typically be quite inelastic and that this condition is quite likely to be met in many cases. 

Price elasticities for activities are generally low when the good is considered a necessity, when substitutes are not available to satisfy perceived need, when the proportion of income spent on the good is low, or when the good is purchased frequently.  A relatively constant quantity of necessities such as access to recreational resources for walking, viewing nature, etc. will be purchased almost irrespective of price, within the price ranges normally encountered.  For these general experiences there are no close substitutes, implying very inelastic price responses.  However, for specific recreation and amenity sites, as with particular entertainment and outdoor sports events, the more substitutes that are available, and the greater the competition, the more the demand for these activities is dependent upon price.  Furthermore, the demand for high priced goods and services, which account for a large proportion of purchasers' incomes, are also relatively sensitive to price.  The price elasticity of demand for boats is typically much higher than those for camping, walking, and viewing nature.  The small percentage of income spent on the latter goods and services means that it is simply not worthwhile spending time and energy worrying about their prices.  

The low price elasticity for generic recreational activities such as walking and nature observation, and amenity demands such as landscape preservation, etc., arise because:
The estimated income elasticities of demand for most recreational goods and services is positive.  Luxury recreational goods have higher income elasticities [indeed this is how they are categorised!].  Income levels have historically doubled every 20 to 30 years in western economies.  Hence, the demand for recreation and amenity goods will increase, not only for urban recreational goods such as theatre trips, restaurant meals, etc., but also for countryside recreational goods such walks, nature observation, and landscape preservation.  As the recreational good becomes more specific and the number of substitutes increases, income elasticity declines.  Thus, estimates of the income elasticity for particular recreational activities and sites is likely to be inelastic, i.e. less than 1.0

However, simple price elasticities tend to be lower than simple income elasticities for environmental goods.  Thus the income flexibility for public goods in the environment is likely to be greater than 1.0.  The demand for such goods is likely to increase substantially over the next 25 years, necessitating environmental control, regulation, and planning, to ensure their long term supply where they are a joint product with agricultural production, and to guard against their short term consumption to the detriment of future demands.

The only caveat to this argument is that long-run elasticities may differ from short run elasticities. Short run demand for recreation and environmental goods is relatively inelastic.  However, over the long run, consumers will adjust their purchases of the environmental or recreational good whose price has risen.  Whilst empirical studies reveal price elasticity of demand for recreational experiences to be inelastic (<1.0) in the short run, it is expected to be elastic (>1.0) in the long run, especially for specific recreational sites and activities with substitutes.  Thus, whilst a 10% increase in the price of consuming a particular type of countryside recreation would result in a 2% decrease in demand in the first year when price is inelastic (-0.2); in the long run a 10% increase in price could reduce recreational demand.   

For instance, suppose that the price elasticity of demand for walking is -0.20 (day outing).  A study by Willis and Garrod (1997) estimated, from a random samples of 932 visitors, that people would be WTP £0.23 to avoid a 1% increase in the number of pipe bridges, pylons, and cable crossings, encountered in walking along canals in the countryside.  Assuming that the direct cost per individual of visiting a canal for a walk is £1.50, then the visual effect of utility service crossing over canals is equivalent to a 15.3p ( = £0.23/£1.50) increase in the 'price' of the walk. 

The visual effect of an increase in utility services crossing across canals continued for a decade: recreational walks along canal towpaths would be expected to decrease by 3.1% ( = 15.3 * 0.20) in the first year; by 6.9% in the second year; and so on until it reached a level of about 19.4% of the original level.  Thus, the long term visual impact of utility service networks is to substantially reduce recreational walks in the countryside, assuming other factors such as population do not change.  Of course, this estimate should be treated as a first approximation, to be verified by future studies of the long-run demand for specific recreation activities and environmental resource attributes.

Willis, K.G. and G.D. Garrod (1997).  Disamenity Externalities from Utility Networks.  Utilities Policy  7
 
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