How would multiplying a positive constant to a linear demand function affect its own-price elasticity of demand? In particular, how would the elasticity of demand of \(Q_{x}=a+bP_{x}+cP_{y}+dI\) at a point compare with the elasticity of demand of the function \(R_{x}=kQ_{x}=ka+kbP_{x}+kcP_{y}+kdI\) hat is evaluated at the same point and k is any positive constant?
The cross-price elasticity of x with respect to Py is different at every point along a linear demand curve. Does this mean that x and y are gross substitutes in one region of the demand curve and gross complements in another region?