Economics/Interpretation of cross elasticity of demand
I have a question relating to the interpretation of cross elasticity of demand.
Cross elasticities of demand for Pork and Beef:
beef with respect to the price of pork 0.10
pork with respect to the price of pork 0.25
In the example above,
(1) Both are substitutes for each other.
(2) There is little relation between pork and beef because of the small value.
Is it correct?
What more can be commented on the values?
I'm afraid that your assumptions for 1 and 2 and contradictions of each other. If pork and beef are substitutes for each other, then there must be a strong relationship between them. The absolute price of each doesn't determine the relationship between substitutes, but the relative price comparison will play a role on the cross elasticity of demand.
Since pork and beef are substitutes for each other, what we're going to be concerned with is their marginal rate of substitution; the amount of utility that people, on average, get from one, and the amount of the other that they must get to equal the same utility. In other words, when choosing between the two, if someone prefers beef, then they must give up more than 1 units of pork to get the same utility as as 1 unit of beef. The rate of substitution will change for each marginal unit, forming the traditional curvilinear relationship that one expects in economics, stemming from a broad application of the law of diminishing marginal utility. Now, of course price plays a role in all this. Price, generally speaking, is a measure of average utility, given that money is a measure of value of resource debt. So, cross elasticity of demand is the rate at which the marginal rate of substitution marginally transforms, with price playing the role of utility.