As shown in the appendix to chapter 4, the Cobb-Douglas form of utility function, U(X,Y) = a log(X) + (1-a) log(Y), yields demand functions X = (a/Px)I and Y = [(1-a)/Py]l. These demand functions have some unique properties. One is that the cross-price elasticities are zero, as pointed out in the appendix, because neither demand depends on the price of the other good. Another unique property is that the own-price elasticities are constant and do not depend on the particular values of the prices and income. Using calculus, the price (Enter your response as real Px ax = elasticity of demand for good X can be calculated as Ep Therefore, the price elasticity of demand for good X equals X OP X number rounded to one decimal place.) The income elasticity of demand also does not depend on the values of prices and income. The income elasticity of demand for good X can be calculated as I ax (Enter your response as a real number rounded to one decimal place.) E₁ = The income elasticity of demand for good X is therefore X di One other unusual property of these demand functions is that the consumer spends a fixed proportion of income on each good regardless of the values of the prices and income. The fraction of income spent on good X is a 1/Px 1/2